Question

Convert 4(cos(240°) + isin(240°)) into rectangular form.

Answer 1

First of all, observe that

$\sin(240)=\sin(-30+270)=-\cos(-30)=-\cos(30)=-\dfrac{\sqrt{3}}{2}$

And similarly,

$\cos(240)=\cos(-30+270)=\sin(-30)=-\sin(30)=-\dfrac{1}{2}$

Now just substitute these values:

$4(\cos(240)+i\sin(240)=4\left(-\dfrac{1}{2}+i\dfrac{-\sqrt{3}}{2}\right) = -2-2i\sqrt{3}$

And since the complex number a+bi is mapped to the point (a,b), the rectangular coordinates are

$(-2, -2\sqrt{3})$