NDA 2021 Maths · Mathematics · Complex Numbers and Quadratic Equations · easy

For any complex number z, |z|^2=zbar z. 2. For any non-zero complex number z, |(z)/(bar z)|=1.

Single correct option

Which of the statements is/are correct? 1. For any complex number

z

|z|^2=z\bar z

. 2. For any non-zero complex number

z

\left|\dfrac{z}{\bar z}\right|=1

Show answer and solution

Answer: (C) Both 1 and 2

Statement 1 is the definition-based identity

z\bar z=x^2+y^2=|z|^2

. Statement 2 holds because

|\bar z|=|z|

, so the ratio of moduli is

1

for every non-zero

z

. Both are correct.

Original question written in the NDA 2021 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