NDA 2017 Maths · Mathematics · Complex Numbers and Quadratic Equations · medium

The smallest positive integer n for which ((1+i)/(√2))^n=1 is

Single correct option

The smallest positive integer

n

for which

\left(\dfrac{1+i}{\sqrt2}\right)^n=1

Show answer and solution

Answer: (D) 8

\frac{1+i}{\sqrt2}=\cos\frac\pi4+i\sin\frac\pi4

, so the

n

th power is

\cos\frac{n\pi}4+i\sin\frac{n\pi}4

. It equals 1 when

\frac{n\pi}4

is a multiple of

2\pi

, i.e.

n=8

n=4

gives

-1

Original question written in the NDA 2017 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