NDA 2025 Maths · Mathematics · Complex Numbers and Quadratic Equations · hard

If z+1/z=√2, then z^2024+(1)/(z^2024) equals

Single correct option

z+\dfrac1z=\sqrt2

, then

z^{2024}+\dfrac1{z^{2024}}

equals

Show answer and solution

Answer: (D) $2$

z+\frac1z=2\cos\theta=\sqrt2

means

z=e^{\pm i\pi/4}

. Then

z^{n}+z^{-n}=2\cos\frac{n\pi}{4}

. For

n=2024=8\cdot253

\frac{n\pi}4=506\pi

and

\cos506\pi=1

, so the value is

2

Original question written in the NDA 2025 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