NDA 2020 Maths · Mathematics · Complex Numbers and Quadratic Equations · easy

For a complex number z: 1. zbar z=|z|^2. 2. |bar z|=|z|.

Single correct option

Consider the following statements for a complex number

z

:
1.

z\bar z=|z|^2

.
2.

|\bar z|=|z|

.
Which of the statements is/are correct?

Show answer and solution

Answer: (C) Both 1 and 2

z=x+iy

then

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

, so statement 1 holds. The conjugate

x-iy

has the same modulus

\sqrt{x^2+y^2}

, so statement 2 also holds. Both are true for every complex

z

, and both are used constantly in simplifying quotients.

Original question written in the NDA 2020 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