4-1.Complex numbers
easy

If $z$ is a complex number, then $(\overline {{z^{ - 1}}} )(\overline z ) = $

A

$1$

B

$-1$

C

$0$

D

None of these

Solution

(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$

Standard 11
Mathematics

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