If and are different complex numbers with | | = 1, then | - 1 - |… - Vidyadip

MCQ

If $\alpha $ and $\beta $ are different complex numbers with $|\beta | = 1$, then $\left| {\frac{{\beta - \alpha }}{{1 - \overline \alpha \beta }}} \right|$ is equal to

A
$0$
B
$3$
✓
$1$
D
$2$

✓

Answer

Correct option: C.

$1$

c
(c) $\frac{{x{x_1}}}{{18}} + \frac{{y{y_1}}}{{32}} = 1$

$ = \frac{1}{{|\beta |}}\left| {\frac{{\beta - \alpha }}{{(\overline {\beta - \alpha } )}}} \right| = \frac{1}{{|\beta |}} = 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 4.1 complex nubers→4.1 complex nubers — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The combined mean of three groups is 12 and the combined mean of first two groups is 3. If the first, second and third group have their mean as 2, 3 and 5 times respectively, then the mean of third group is:

Let $\alpha$ and $\beta$ be the roots of the equation $\mathrm{px}^2+\mathrm{qx}-$ $r=0$, where $p \neq 0$. If $p, q$ and $r$ be the consecutive terms of a non-constant G.P and $\frac{1}{\alpha}+\frac{1}{\beta}=\frac{3}{4}$, then the value of $(\alpha-\beta)^2$ is :

If D, G and R denote respectively the number of degrees, grades and radians in an angle, then:

From the origin, chords are drawn to the circle ${(x - 1)^2} + {y^2} = 1$. The locus of mid points of these chords is a

If $a, b, c$ are in A.P. and $x, y, z$ are in G.P., then the value of $x^{b-c} y^{c-a} z^{a-b}$ is:

If $ \tan\ \theta _1. tan \theta _2 $ $= -\frac{{{a^2}}}{{{b^2}}}$ then the chord joining two points $\theta _1 \& \theta _2$ on the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}}$ $= 1$ will subtend a right angle at :

If $tan\, \alpha = \frac{{{x^2} - x}}{{{x^2} - x + 1}}$ and $tan \, \beta =$ $\frac{1}{{2{x^2} - 2x + 1}}$ $(x \ne 0, 1)$, where $0 < \alpha , \beta < \frac{\pi }{2}$, then $tan(\alpha + \beta )$ has the value equal to :

Which term of G.P. 25, 125, 625, …………. is 390625?

Two card are drawn successively with replacement from a pack of $52$ cards. The probability of drawing two aces is

If $\mathop {\lim }\limits_{x \to \infty } {\left( {\frac{{{a^{1/x}} + b}}{c}} \right)^x} = d$ (non zero finite), then $(b + 1)log_a\,d$ is