NDA 2023 Maths · Mathematics · Complex Numbers and Quadratic Equations · medium

The value of ((1+i)/(1-i))^2023 is

Single correct option

The value of

\left(\dfrac{1+i}{1-i}\right)^{2023}

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Answer: (B) $-i$

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

. Powers of

i

repeat with period

4

, and

2023=4\cdot505+3

, so

i^{2023}=i^3=-i

. Picking

i

comes from reducing the exponent as

2023\equiv1

Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake