Download App

STD 11 - 4.1 complex nubers — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 4.1 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$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 11 - 4.1 complex nubers→STD 11 - 4.1 complex nubers — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

${x^2} - 11x + a$ and ${x^2} - 14x + 2a$will have a common factor, if $a = $
→
The distance from the centre of the circle $x^2 + y^2 = 2x$ to the straight line passing  through the points of intersection of the two circles $x^2 + y^2 + 5x -8y + 1 =0$ and $x^2 + y^2-3x + 7y -25 = 0$ is-
→
Let $R = (a, b, c, d)$ and $S = (1, 2, 3),$ then the number of functions $f,$ from $R$ to $S,$ which are onto is:
→
Which of the following is the inverse of the proposition: “If a number is a prime then it is odd.”
→
Argument of $ - 1 - i\sqrt 3 $ is
→
Let $S$ be the sum, $P$ be the product and $R$ be the sum of the reciprocals of $3$ terms of a $G.P.$ then $\ce{P^2R^3 : S^3}$ is equal to:
→
If ${\log _{\sqrt 3 }}\left( {\frac{{|z{|^2} - |z| + 1}}{{2 + |z|}}} \right) < 2$, then the locus of $z$ is
→
In the expansion of ${\left( {\frac{{1 + x}}{{1 - x}}} \right)^2}$, the coefficient of ${x^n}$ will be
→
The sum of $100$ observations and the sum of their squares are $400$ and $2475$, respectively. Later on, three observations, $3, 4$ and $5$, were found to be incorrect . If the incorrect observations are omitted, then the variance of the remaining observations is
→
If the sum of the binomial coefficients of the expansion $\Big(2\text{x}+\frac{1}{\text{x}}\Big)^{\text{n}}$ is equal to $256,$ then the term independent of $x$ is:
→