How do I solve this to represent the complex number in Cartesian coordinate
$$z=\frac{e^{\frac{\pi}{3}i}}{e^{\frac{2}{3}\pi i}\cdot 2e^{\frac{\pi}{6}i}}$$
So I got this question as a homework and I am not able to solve it correctly. Any leads on how to solve this would help.
Hint: For any $x\in\mathbb R$, you have
$$e^{ix}=\cos(x)+i\sin(x)$$
also known as Euler's formula.
So, e.g. considering $e^{\frac{\pi}{3}i}$, as $\pi/3\in\mathbb R$, we have
$$e^{\frac{\pi}{3}i}=\cos(\pi/3)+i\sin(\pi/3)=\frac{1}{2}+i\frac{\sqrt{3}}{2}$$
You can proceed to use this conversion of polar to cartesian representations to convert the other expressions. Then, you may proceed to do arithmetic on those cartesian-represented numbers as usual.