JEE Main 2022 · Mathematics · Complex Numbers · easy

The value of ((1+i)/(1-i))^2022 is

Single correct option

The value of

\left(\dfrac{1+i}{1-i}\right)^{2022}

Show answer and solution

Answer: (B) $-1$

Simplify the base:

\frac{1+i}{1-i}=\frac{(1+i)^2}{2}=\frac{2i}{2}=i

. Hence the expression is

i^{2022}

. Since powers of

i

repeat with period 4 and

2022=4(505)+2

i^{2022}=i^2=-1

. Shortcut: reduce the exponent modulo 4 after recognising the base equals

i

Original question written in the JEE Main 2022 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake