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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, then $(\overline {{z^{ - 1}}} )(\overline z ) = $
  • ✓
    $1$
  • B
    $-1$
  • C
    $0$
  • D
    None of these
✓

Answer

Correct option: A.
$1$
a
(a) Let $z = x + iy,\overline z = x - iy$ and ${z^{ - 1}} = \frac{1}{{x + iy}}$
==> $(\overline {{z^{ - 1}}} ) = \frac{{x + iy}}{{{x^2} + {y^2}}}$; $\therefore $$(\overline {{z^{ - 1}}} )\,\bar z = \frac{{x + iy}}{{{x^2} + {y^2}}}(x - iy) = 1$

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