Complex numbers z=-3-4i polar form Unicorn Meta Zoo #1: Why another podcast? ...

Why do distances seem to matter in the Foundation world?

How do I check if a string is entirely made of the same substring?

"My boss was furious with me and I have been fired" vs. "My boss was furious with me and I was fired"

Multiple fireplaces in an apartment building?

What's the difference between using dependency injection with a container and using a service locator?

Why didn't the Space Shuttle bounce back into space as many times as possible so as to lose a lot of kinetic energy up there?

Negative Resistance

Where was the County of Thurn und Taxis located?

Should the Product Owner dictate what info the UI needs to display?

A strange hotel

Why do games have consumables?

Older movie/show about humans on derelict alien warship which refuels by passing through a star

Will I lose my paid in full property

How to keep bees out of canned beverages?

std::unique_ptr of base class holding reference of derived class does not show warning in gcc compiler while naked pointer shows it. Why?

Is Electric Central Heating worth it if using Solar Panels?

Bayes factor vs P value

Combinatorics problem, right solution?

Is this homebrew arcane communication device abusable?

How does the mezzoloth's teleportation work?

As an international instructor, should I openly talk about my accent?

How long after the last departure shall the airport stay open for an emergency return?

First instead of 1 when referencing

The weakest link



Complex numbers z=-3-4i polar form



Unicorn Meta Zoo #1: Why another podcast?
Announcing the arrival of Valued Associate #679: Cesar ManaraExpressing $e^z$ where $z=a+bi$ in polar form.Polar form of Complex numbersConverting to polar formComplex number polar form equationWhy is e used for polar form of complex numbers?Show $-27$ in polar form.writing in polar form (complex numbers)Are all complex exponentials in polar form?Complex numbers polar form changeDifferentiating polar functions using complex numbers












4












$begingroup$


$z=-3-4i$ . In polar form this becomes $[5, 233° ]$. The question then asks for $z^2$, so the polar form becomes $[25,466]$ However in the solution they did $466° -360° $ and I am unsure why they did this. Is it a rule that needs to be applied.






complex-numbers polar-coordinates







share|cite|improve this question











$endgroup$

















    4












    $begingroup$


    $z=-3-4i$ . In polar form this becomes $[5, 233° ]$. The question then asks for $z^2$, so the polar form becomes $[25,466]$ However in the solution they did $466° -360° $ and I am unsure why they did this. Is it a rule that needs to be applied.






    complex-numbers polar-coordinates







    share|cite|improve this question











    $endgroup$















      4












      4








      4





      $begingroup$


      $z=-3-4i$ . In polar form this becomes $[5, 233° ]$. The question then asks for $z^2$, so the polar form becomes $[25,466]$ However in the solution they did $466° -360° $ and I am unsure why they did this. Is it a rule that needs to be applied.






      complex-numbers polar-coordinates







      share|cite|improve this question











      $endgroup$




      $z=-3-4i$ . In polar form this becomes $[5, 233° ]$. The question then asks for $z^2$, so the polar form becomes $[25,466]$ However in the solution they did $466° -360° $ and I am unsure why they did this. Is it a rule that needs to be applied.






      complex-numbers polar-coordinates




      complex-numbers polar-coordinates






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited 1 hour ago









      José Carlos Santos

      178k24139251




      178k24139251










      asked 1 hour ago









      user221435user221435

      285




      285






















          2 Answers
          2






          active

          oldest

          votes


















          3












          $begingroup$

          It's because$$cos(x-360^circ)=cos(x)text{ and }sin(x-360^circ)=sin(x).$$






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            Usually I don't do this when I get the degree, why is it that in this case I needed to do this?
            $endgroup$
            – user221435
            1 hour ago






          • 2




            $begingroup$
            We don't need to do this, but we usually try to work with angles in the range $[0^circ,360^circ)$.
            $endgroup$
            – José Carlos Santos
            1 hour ago










          • $begingroup$
            Great, thank you
            $endgroup$
            – user221435
            1 hour ago



















          2












          $begingroup$

          It is just to get the principal value of the angle, since if you rotate by an angle $466^{circ}$ you'll get to the same position as rotating $106^{circ}$ so we usually take the smallest angle that is needed to arrive at the desired position.



          The principal angle is an angle between $-180^{circ}$ and $+180^{circ}$






          share|cite|improve this answer











          $endgroup$














            Your Answer








            StackExchange.ready(function() {
            var channelOptions = {
            tags: "".split(" "),
            id: "69"
            };
            initTagRenderer("".split(" "), "".split(" "), channelOptions);

            StackExchange.using("externalEditor", function() {
            // Have to fire editor after snippets, if snippets enabled
            if (StackExchange.settings.snippets.snippetsEnabled) {
            StackExchange.using("snippets", function() {
            createEditor();
            });
            }
            else {
            createEditor();
            }
            });

            function createEditor() {
            StackExchange.prepareEditor({
            heartbeatType: 'answer',
            autoActivateHeartbeat: false,
            convertImagesToLinks: true,
            noModals: true,
            showLowRepImageUploadWarning: true,
            reputationToPostImages: 10,
            bindNavPrevention: true,
            postfix: "",
            imageUploader: {
            brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
            contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
            allowUrls: true
            },
            noCode: true, onDemand: true,
            discardSelector: ".discard-answer"
            ,immediatelyShowMarkdownHelp:true
            });


            }
            });














            draft saved

            draft discarded


















            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3202145%2fcomplex-numbers-z-3-4i-polar-form%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown

























            2 Answers
            2






            active

            oldest

            votes








            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            3












            $begingroup$

            It's because$$cos(x-360^circ)=cos(x)text{ and }sin(x-360^circ)=sin(x).$$






            share|cite|improve this answer









            $endgroup$













            • $begingroup$
              Usually I don't do this when I get the degree, why is it that in this case I needed to do this?
              $endgroup$
              – user221435
              1 hour ago






            • 2




              $begingroup$
              We don't need to do this, but we usually try to work with angles in the range $[0^circ,360^circ)$.
              $endgroup$
              – José Carlos Santos
              1 hour ago










            • $begingroup$
              Great, thank you
              $endgroup$
              – user221435
              1 hour ago
















            3












            $begingroup$

            It's because$$cos(x-360^circ)=cos(x)text{ and }sin(x-360^circ)=sin(x).$$






            share|cite|improve this answer









            $endgroup$













            • $begingroup$
              Usually I don't do this when I get the degree, why is it that in this case I needed to do this?
              $endgroup$
              – user221435
              1 hour ago






            • 2




              $begingroup$
              We don't need to do this, but we usually try to work with angles in the range $[0^circ,360^circ)$.
              $endgroup$
              – José Carlos Santos
              1 hour ago










            • $begingroup$
              Great, thank you
              $endgroup$
              – user221435
              1 hour ago














            3












            3








            3





            $begingroup$

            It's because$$cos(x-360^circ)=cos(x)text{ and }sin(x-360^circ)=sin(x).$$






            share|cite|improve this answer









            $endgroup$



            It's because$$cos(x-360^circ)=cos(x)text{ and }sin(x-360^circ)=sin(x).$$







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered 1 hour ago









            José Carlos SantosJosé Carlos Santos

            178k24139251




            178k24139251












            • $begingroup$
              Usually I don't do this when I get the degree, why is it that in this case I needed to do this?
              $endgroup$
              – user221435
              1 hour ago






            • 2




              $begingroup$
              We don't need to do this, but we usually try to work with angles in the range $[0^circ,360^circ)$.
              $endgroup$
              – José Carlos Santos
              1 hour ago










            • $begingroup$
              Great, thank you
              $endgroup$
              – user221435
              1 hour ago


















            • $begingroup$
              Usually I don't do this when I get the degree, why is it that in this case I needed to do this?
              $endgroup$
              – user221435
              1 hour ago






            • 2




              $begingroup$
              We don't need to do this, but we usually try to work with angles in the range $[0^circ,360^circ)$.
              $endgroup$
              – José Carlos Santos
              1 hour ago










            • $begingroup$
              Great, thank you
              $endgroup$
              – user221435
              1 hour ago
















            $begingroup$
            Usually I don't do this when I get the degree, why is it that in this case I needed to do this?
            $endgroup$
            – user221435
            1 hour ago




            $begingroup$
            Usually I don't do this when I get the degree, why is it that in this case I needed to do this?
            $endgroup$
            – user221435
            1 hour ago




            2




            2




            $begingroup$
            We don't need to do this, but we usually try to work with angles in the range $[0^circ,360^circ)$.
            $endgroup$
            – José Carlos Santos
            1 hour ago




            $begingroup$
            We don't need to do this, but we usually try to work with angles in the range $[0^circ,360^circ)$.
            $endgroup$
            – José Carlos Santos
            1 hour ago












            $begingroup$
            Great, thank you
            $endgroup$
            – user221435
            1 hour ago




            $begingroup$
            Great, thank you
            $endgroup$
            – user221435
            1 hour ago











            2












            $begingroup$

            It is just to get the principal value of the angle, since if you rotate by an angle $466^{circ}$ you'll get to the same position as rotating $106^{circ}$ so we usually take the smallest angle that is needed to arrive at the desired position.



            The principal angle is an angle between $-180^{circ}$ and $+180^{circ}$






            share|cite|improve this answer











            $endgroup$


















              2












              $begingroup$

              It is just to get the principal value of the angle, since if you rotate by an angle $466^{circ}$ you'll get to the same position as rotating $106^{circ}$ so we usually take the smallest angle that is needed to arrive at the desired position.



              The principal angle is an angle between $-180^{circ}$ and $+180^{circ}$






              share|cite|improve this answer











              $endgroup$
















                2












                2








                2





                $begingroup$

                It is just to get the principal value of the angle, since if you rotate by an angle $466^{circ}$ you'll get to the same position as rotating $106^{circ}$ so we usually take the smallest angle that is needed to arrive at the desired position.



                The principal angle is an angle between $-180^{circ}$ and $+180^{circ}$






                share|cite|improve this answer











                $endgroup$



                It is just to get the principal value of the angle, since if you rotate by an angle $466^{circ}$ you'll get to the same position as rotating $106^{circ}$ so we usually take the smallest angle that is needed to arrive at the desired position.



                The principal angle is an angle between $-180^{circ}$ and $+180^{circ}$







                share|cite|improve this answer














                share|cite|improve this answer



                share|cite|improve this answer








                edited 1 hour ago









                J. W. Tanner

                5,2001520




                5,2001520










                answered 1 hour ago









                Fareed AFFareed AF

                1,025214




                1,025214






























                    draft saved

                    draft discarded




















































                    Thanks for contributing an answer to Mathematics Stack Exchange!


                    • Please be sure to answer the question. Provide details and share your research!

                    But avoid …



                    • Asking for help, clarification, or responding to other answers.

                    • Making statements based on opinion; back them up with references or personal experience.


                    Use MathJax to format equations. MathJax reference.


                    To learn more, see our tips on writing great answers.




                    draft saved


                    draft discarded














                    StackExchange.ready(
                    function () {
                    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3202145%2fcomplex-numbers-z-3-4i-polar-form%23new-answer', 'question_page');
                    }
                    );

                    Post as a guest















                    Required, but never shown





















































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown

































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown







                    -

                    Popular posts from this blog

                    Gersau Kjelder | Navigasjonsmeny46°59′0″N 8°31′0″E46°59′0″N...

                    Image
                    Tidlegare republikkarSkipingar i 1433Kommunar i SchwyzDistrikt i SchwyzNedleggingar i 1798Stader ved Vierwaldstättersee kommunekantonenSchwyzSveitskm²VierwaldstätterseeLauerz Gersau Kommunevåpenet til Gersau Plassering Styresmakter Land   Sveits Kanton kantonen Schwyz Distrikt Gersau Språk tysk Geografi Flatevidd  - kommune 23,70 km² Innbyggjarar  - kommune (desember 2010)    - folketettleik 2 094   88,4 /km² Koordinatar 46°59′0″N 8°31′0″E  Koordinatar: 46°59′0″N 8°31′0″E  Høgd over havet 435 moh Diverse annan informasjon Postnummer 6442 Nettstad: www.gersau.ch Freistaat und Republik Gersau Fristaten og republikken Gersau By-republikk og alliert protektorat i Det gamle sveitsiske eidsforundet ←   ← 1433–1798 1814–1818 →   → Hovudstad Gersau Styreform Republikk Historisk periode Tidleg moderne tid  - Kjøpte fridom frå
                    Read more

                    Hestehale Innhaldsliste Hestehale på kvinner | Hestehale på menn | Galleri | Sjå òg |...

                    Image
                    Frisyrar frisyrehårhårstrikkhårklemmerøyrethesthovudverkeuropeisk motejobbtreningfletterparykkarungdomsopprørmotkulturmusikararmotorsykkelentusiastarpolitietpolitiskforretningverksemdfiskeflette Hestehale sett bakfrå. Hestehale på ein mannleg indianarleiar. Hestehale er ein frisyre der ein samlar det meste eller alt av langt hår [1] i bakhovudet med ein hårstrikk eller liknande. Avhengig av mote kan det òg vere vanleg å sette opp hestehalen med hårklemmer eller å ha hestehalen hengande på den eine sida av hovudet ved å samle håret ved øyret. Hestehale er ein vanleg frisyre for jenter og for gutar med langt hår. Han har fått namnet sitt etter likskapen med halen på ein hest. For stramme hestehaler kan føre til hårtap, [2] i nokre høve også hovudverk. [3] Innhaldsliste 1 Hestehale på kvinner 2 Hestehale på menn 3 Galleri 4 Sjå òg 5 Bakgrunnsstoff 6 Kjelder Hestehale på kvinner | Ungjente med hestehale som held håret unna ansiktet
                    Read more

                    What is the “three and three hundred thousand syndrome”?Who wrote the book Arena?What five creatures were...

                    Image
                    What happens when the centripetal force is equal and opposite to the centrifugal force? Why is "la Gestapo" feminine? Nested Dynamic SOQL Query How are passwords stolen from companies if they only store hashes? Exposing a company lying about themselves in a tightly knit industry: Is my career at risk on the long run? Can "few" be used as a subject? If so, what is the rule? Why are there no stars visible in cislunar space? categorizing a variable turns it from insignificant to significant Do I need an EFI partition for each 18.04 ubuntu I have on my HD? What are the consequences of changing the number of hours in
                    Read more