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4.1 complex nubers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.1 complex nubers1 Mark
MCQ
If $z$ is a complex number such that ${z^2} = {(\bar z)^2},$ then
  • A
    $z$ is purely real
  • B
    $z$ is purely imaginary
  • ✓
    Either $z$ is purely real or purely imaginary
  • D
    None of these
✓

Answer

Correct option: C.
Either $z$ is purely real or purely imaginary
c
(c)Let $z = x + iy$, then its conjugate $\overline z = x - iy$
Given that ${z^2} = {(\overline z )^2}$
==> ${x^2} - {y^2} + 2ixy = {x^2} - {y^2} - 2ixy$==> $4ixy = 0$
If $x \ne 0$ then $y = 0$and if $y \ne 0$then $x = 0$
.

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