NDA 2019 Maths · Mathematics · Complex Numbers and Quadratic Equations · hard

If z+1/z=1, then z^12 equals

Single correct option

z+\dfrac1z=1

, then

z^{12}

equals

Show answer and solution

Answer: (D) $1$

From

z^2-z+1=0

we get

z=\dfrac{1\pm i\sqrt3}{2}=\cos\dfrac\pi3\pm i\sin\dfrac\pi3

. Then

z^{12}=\cos4\pi\pm i\sin4\pi=1

. Alternatively

z^3=-1

(multiply by

z+1

), so

z^6=1

and

z^{12}=1

. The value

-1

z^3

, a common stop-short error.

Original question written in the NDA 2019 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