Question

Use a scientific calculator or unit circle to convert the polar form of the complex number to its equivalent rectangular

Answer 1

Since 210=180+30, we have

$\cos(210)=-\cos(30)=-\dfrac{\sqrt{3}}{2}$

$\cos(210)=-\sin(30)=-\dfrac{1}{2}$

So, we have

$z=2\left(-\dfrac{\sqrt{3}}{2} - \dfrac{i}{2}\right) = -\sqrt{3}-i$