anonymous
  • anonymous
Write the following complex number in polar form. Express all angles in degrees rounded to the nearest tenth. –3
Mathematics
chestercat
  • chestercat
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zepdrix
  • zepdrix
\[\Large\rm -3=\color{royalblue}{3}\cdot\color{orangered}{(-1)}=\color{royalblue}{r}\cdot\color{orangered}{e^{i?}}\]
zepdrix
  • zepdrix
You have learned about the exponential form, or no?
zepdrix
  • zepdrix
\[\large\rm \color{royalblue}{3}\cdot\color{orangered}{(-1)}=\color{royalblue}{r}\color{orangered}{(\cos \theta+i \sin \theta)}\]Maybe this breakdown is unnecessary. -3 is along the real axis. So what angle is that? :)

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zepdrix
  • zepdrix
|dw:1441669382809:dw|
anonymous
  • anonymous
yes, i know what exponential form. the angle would be 180 degrees, yes? but how do i write the entire answer?
zepdrix
  • zepdrix
|dw:1441670191367:dw|\[\large\rm \color{royalblue}{r}\color{orangered}{(\cos \theta+i \sin \theta)}=\color{royalblue}{3}\cdot\color{orangered}{(-1)}=\color{royalblue}{3}\cdot\color{orangered}{(\cos180+i \sin180)}\]
zepdrix
  • zepdrix
Yes 180, good! :)
anonymous
  • anonymous
so polar form is just 180degrees?
zepdrix
  • zepdrix
No, the polar form is everything on the right of that last equals sign. \[\large\rm -3=3(\cos180^o+i \sin 180^o)\]
anonymous
  • anonymous
so that's my answer? 3 (cos180° +i sin180°) ?

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