Question

2sqrt3 +2i to polar representation

Answer 1

Recall that

`\cos\frac\pi6=\frac{\sqrt3}2`

`\sin\frac\pi6=\frac12`

Then

`2\sqrt3+2i=4\left(\frac{\sqrt3}2+\frac12i\right)=4\left(\cos\frac\pi6+i\sin\frac\pi6\right)=4e^(i\pi/6)`