Imaginary of complex coordinates

Question

Hi I'm wondering how to find the value of Im(a). Is that just the y value of the coordinate of a. This is all the problem has given me. I'm confused in terms of how to solve it. FYI the hexagon is regular with a side length of $\sqrt2$

Answer 1

The interior angles are all $120^0$ (you can divide the hexagon into $4$ triangles). $1-i=\sqrt2 e^{-\frac{\pi i}4}$.

Therefore, $\operatorname{arg}a=\frac{2\pi}3-\frac{\pi}4=\frac{5\pi}{12}$.