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)=-(√(3))/(2)`

And similarly,

`\cos(240)=\cos(-30+270)=\sin(-30)=-\sin(30)=-(1)/(2)`

Now just substitute these values:

`4(\cos(240)+i\sin(240)=4\left(-(1)/(2)+i(-√(3))/(2)\right) = -2-2i√(3)`

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

`(-2, -2√(3))`