If z is a complex number, then ( z^ -1 )(z)= - Vidyadip

MCQ

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

✓
1
B
-1
C
$0$
D
i

✓

Answer

Correct option: A.

1

(A)
Let $z =x+ i y$. Then, $\overline{ z }=x- i y$ and $z ^{-1}=\frac{1}{x+ i y}$
$\Rightarrow\left(\overline{ z ^{-1}}\right)=\frac{1}{x- i y} \Rightarrow\left(\overline{ z ^{-1}}\right)=\frac{x+ i y}{x^2+y^2}$
$\therefore \quad\left(\overline{ z ^{-1}}\right) \overline{ z }=\frac{x+ i y}{x^2+y^2}(x- i y)=1$

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 "MCQ" from Complex Numbers→Complex Numbers — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Radius parametric equation represented by $x=2 a\left(\frac{1-t^2}{1+t^2}\right), y=\frac{4 a t}{1+t^2}$ is

$\left|\begin{array}{lll}b+c & c+a & a+b \\ q+r & r+p & p+q \\ y+z & z+x & x+y\end{array}\right|=$

If tangents are drawn to the circle $x^2+y^2=12$ at the points where it intersects the circle $x^2+y^2-5 x+3 y-2=0$, then the coordinates of the point of intersection of those tangents are

If five dice are thrown simultaneously, then the probability that atleast three of them show the same numbered face is

Equation of the hyperbola with eccentricity $\frac{3}{2}$ and foci $( \pm 2,0)$ is

The point A is (3, 0) and abscissa of the point B is -3. A variable point P is such that ordinates of P and B are equal, then equation of locus of P such that AP = PB is

For two given events A and $B , P ( A \cap B )=$

The value of $({^\text{7}}\text{C}_{\text{0}}+{^\text{7}}\text{C}_{\text{1}})+({^\text{7}}\text{C}_{\text{1}}+{^\text{7}}\text{C}_{\text{3}})+.....+({^\text{7}}\text{C}_{\text{6}}+{^\text{7}}\text{C}_{\text{7}})$ is :

If $\operatorname{cosec} \theta=\frac{p+q}{p-q}$, then $\cot \left(\frac{\pi}{4}+\frac{\theta}{2}\right)=$

If $\sin(\pi\cos\text{x})=\cos(\pi\sin\text{x}),$ then $\sin2\text{x}=$