If z is a non-zero complex number, then | | z |^2 z z | is equal … - Vidyadip

MCQ

If $z$ is a non$-$zero complex number, then $\Big|\frac{|\bar{\text{z}}|^2}{\text{z}\bar{\text{z}}}\Big|$ is equal to:

✓
$\Big|\frac{\bar{\text{z}}}{\text{z}}\Big|$
B
$\big|{\text{z}}\big|$
C
$\big|{\bar{\text{z}}}\big|$
D
none of these

✓

Answer

Correct option: A.

$\Big|\frac{\bar{\text{z}}}{\text{z}}\Big|$

$\Big|\frac{|\bar{\text{z}}|^2}{\text{z}\bar{\text{z}}}\Big|=\Big|\frac{|\bar{\text{z}}|^2}{|\text{z}|^2}\Big| \ \Big(\because\text{z}\bar{\text{z}}=|\text{z}|^2\Big)$
Let $\text{z}=\text{a}+\text{ib}$
$\Rightarrow|\text{z}|=\sqrt{\text{a}^2+\text{b}^2}$
Let $\bar{\text{z}}=\text{a}-\text{ib}$
$\Rightarrow|\bar{\text{z}}|=\sqrt{\text{a}^2+\text{b}^2}$
$\therefore\Big|\frac{|\bar{\text{z}}|^2}{\text{z}\bar{\text{z}}}\Big|=\Big|\frac{|\bar{\text{z}}|^2}{|\text{z}|^2}\Big|$
$=\Big|\frac{\bar{\text{z}}}{\text{z}}\Big|$

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 Complex Numbers and Quadratic Equations→Complex Numbers and Quadratic Equations — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

If $n$ is an integer lying between $0$ and $21,$ then the least value of $n!(21 - n)!$ is:

In a series of $3n$ observations, if $n$ observations are equal $a$ and remaining observations are equal $-2a$, then the mean deviation of observations about their mean will be:-

Consider all natural number whose decimal expansion has only the even digits $0,2,4,6,8$. Suppose these are arranged in increasing order. If $a _n$ denotes the $n$th number in this sequence, then $\frac{\lim _{n \rightarrow \infty} \log a_n}{\log n}$ equals

let $x_1, x_2, ...,x_n$ be $n$ observations and $\overline{\text{X}}$ be their arithmetic mean. The standard deviation is given by:

Let the foci of a hyperbola $\mathrm{H}$ coincide with the foci of the ellipse $E: \frac{(x-1)^2}{100}+\frac{(y-1)^2}{75}=1$ and the eccentricity of the hyperbola $\mathrm{H}$ be the reciprocal of the eccentricity of the ellipse $E$. If the length of the transverse axis of $\mathrm{H}$ is $\alpha$ and the length of its conjugate axis is $\beta$, then $3 \alpha^2+2 \beta^2$ is equal to :

If the centroid of an equilateral triangle is $(1, 1)$ and its one vertex is $(−1,2)$ then the equation of its circumcircle is:

If $a, b$ and $c$ be three distinct numbers in $G.P.$ and $a + b + c = xb$ then $x$ can not be

A country has ten smart cities. The government decides to connect all these cities by road. How many roads the government need to construct so that every city is connected to every other city ?

The locus of $z$ satisfying the inequality ${\log _{1/3}}|z + 1|\, > $ ${\log _{1/3}}|z - 1|$ is

The value of $\frac{(\text{i}^5+\text{i}^6+\text{i}^7+\text{i}^8+\text{i}^9)}{(1+\text{i})}$ is: