Consider the complex number (i-1)/(cos π/3 + i sin π/3)

Question

Consider the complex number \(\frac{i-1}{cos \frac{\pi}{3} + i sin \frac{\pi}{3}}\)

1. Express in a + ib form.

2. Convert into polar form.

Answer 1

1. \(\frac{i-1}{cos \frac{\pi}{3} + i sin \frac{\pi}{3}}\) = \(\frac{i-1}{\frac{1}{2} + i \frac{\sqrt 3}{2}}\) = \(\frac{2(i-1)}{1 + i \sqrt{3}}\)

2. 

The complex number lies in the first quadrant;

⇒ θ = α = \(\frac{5 \pi}{12}\)