Download App

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

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 4.1 complex nubers4 Marks
MCQ
$\left| {(1 + i)\frac{{(2 + i)}}{{(3 + i)}}} \right| = $
  • A
    $ - \frac{1}{2}$
  • B
    $\frac{1}{2}$
  • ✓
    $1$
  • D
    $ - 1$
✓

Answer

Correct option: C.
$1$
c
(c)$\left| {(1 + i)\frac{{(2 + i)}}{{(3 + i)}}} \right| = |1 + i|\left| {\frac{{2 + i}}{{3 + i}}} \right| = \frac{{\sqrt 2 \times \sqrt 5 }}{{\sqrt {10} }} = 1$
.

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $y = {\sin ^{ - 1}}{{\sqrt {(1 + x)} + \sqrt {(1 - x)} } \over 2}$, then ${{dy} \over {dx}} = $
→
If $f(x) = 3{e^{{x^2}}}$, then $f'(x) - 2xf(x) + {1 \over 3}f(0) - f'(0) = $
→
Let $y=y(x)$ be the solution of the differential equation $ \frac{d y}{d x}=\frac{(\tan x)+y}{\sin x(\sec x-\sin x \tan x)}$, $x \in\left(0, \frac{\pi}{2}\right)$ satisfying the condition $y\left(\frac{\pi}{4}\right)=2$. Then, $y\left(\frac{\pi}{3}\right)$ is
→
If in a triangle $ABC$, $A = {\tan ^{ - 1}}2$ and $B = {\tan ^{ - 1}}3,$ then angle $C$ is equal to
→
The sides of a right angled triangle are in arithmetic progression. If the triangle has area $24$ , then what is the length of its smallest side ?
→
Let $P = \left\{ {\theta :\sin \,\theta  - \cos \,\theta  = \sqrt 2 \,\cos \,\theta } \right\}$ and $Q = \left\{ {\theta :\sin \,\theta  + \cos \,\theta  = \sqrt {2\,} \sin \,\theta } \right\}$ be two sets. Then
→
Let $\lambda, \mu \in R$. If the system of equations

$ 3 x+5 y+\lambda z=3 $

$ 7 x+11 y-9 z=2 $

$ 97 x+155 y-189 z=\mu$

has infinitely many solutions, then $\mu+2 \lambda$ is equal to :

→
Which of the following statements could be true if, $f'' (x) = x^{1/3}$.  

$I$ $II$ $III$ $IV$
$f'(x) = \frac{9}{{28}} x^{7/3} +9$ $f (x) = \frac{9}{{28}} x^{7/3} -2$  $f (x) = \frac{3}{{4}}\,x^{4/3} +6$ $f'(x) =\frac{3}{{4}}\,x^{4/3} -4$

 

→
Differential coefficient of ${{{{\tan }^{ - 1}}x} \over {1 + {{\tan }^{ - 1}}x}}$ w.r.t. ${\tan ^{ - 1}}x$ is
→
If $x_1 , y_1$ are the roots of $x^2 + 8 x - 20 = 0$ ,$ x_2 , y_2$ are the roots of $4 x^2 + 32 x - 57 = 0$ and $x_3 , y_3$ are the roots of $9 x^2 + 72  x- 112 = 0$ , then the points, $(x_1 , y_1) , (x_2 , y_2) \& (x_3 , y_3)$
→