Question

If \({\rm{z}} + {\rm{\bar z}} = 0\), then
1. Re (z) = 0
2. Im (z) = 0
3. Re (z) + Im (z) = 0
4. Re (z) = Im (z) = 0
5. None of these

Answer 1

Correct Answer - Option 1 : Re (z) = 0

Concept:

Let z = x + iy be a complex number, Where x is called real part of complex number or Re (z) and y is called Imaginary part of the complex number or Im (z)

Conjugate of a complex number:  Conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign

Conjugate of z = \({\rm{\bar z}}\) = x – iy

Calculation:

Let z = x + iy

Then  \({\rm{\bar z}}\) = x – iy

Given: \({\rm{z}} + {\rm{\bar z}} = 0\)

⇒ (x + iy) + (x – iy) = 0

⇒ 2x = 0

⇒ x = 0

∴ Re (z) = 0