Question

Express the following in the form a + ib, a, b ∈ R, using De Moivre’s theorem. (1 - i)⁵

Answer 1

Let z = 1 - i

\(\therefore\) a = 1, b = -1, i.e. a >0, b < 0

\(\therefore\) |z| = \(\sqrt{a^2+b^2}=\sqrt{1^2+(-1)^2}=\sqrt2\) 

Here, (1, -1) lies in 4^th quadrant.

= -4 + 4i