Question

Simplify the following expressions:

(a) (cos π/4 + i sin π/4)(cos 3π/4 + i sin 3π/4), (b) (cos π/4 + i sin π/4)2

(cos π/6 + i sin π/6)

Answer 1

Answers:

(a) $(cos\frac{\pi}{4}+i\sin\frac{\pi}{4})(cos\frac{3\pi}{4}+i\sin\frac{3\pi}{4})= (\frac{\sqrt{2}}{2}+i\frac{\sqrt{2}}{2})(-\frac{\sqrt{2}}{2}+i\frac{\sqrt{2}}{2})=$

$=-1$

(b)$2(cos\frac{\pi}{4}+i\sin\frac{\pi}{4})=\sqrt{2}+i\sqrt{2}$

$cos\frac{\pi}{6}+i\,sin\frac{\pi}{6}=\frac{\sqrt{3}}{2}+i\frac{1}{2}$