Write in $a+ib$ form the following number $\cos ( \frac{\pi}{3} + iLog(4))$

Question

I have to write in $a+ib$ form the following number $\cos ( \frac{\pi}{3} + iLog(4))$. How do I start? Can anyone help?

Answer 1

HINT: $$\cos z=1/2(e^{iz}+e^{-iz}),z\in \mathbb{C}\\e^{ix}=\cos x+i\sin x ,x\in\mathbb{R}$$