If |z - 25i| 15, then | .amp(z) - .amp(z)| = - Vidyadip

MCQ

If $|z - 25i| \le 15$, then $|\max .amp(z) - \min .amp(z)| = $

A
${\cos ^{ - 1}}\left( {\frac{3}{5}} \right)$
✓
$\pi - 2{\cos ^{ - 1}}\left( {\frac{3}{5}} \right)$
C
$\frac{\pi }{2} + {\cos ^{ - 1}}\left( {\frac{3}{5}} \right)$
D
${\sin ^{ - 1}}\left( {\frac{3}{5}} \right) - {\cos ^{ - 1}}\left( {\frac{3}{5}} \right)$

✓

Answer

Correct option: B.

$\pi - 2{\cos ^{ - 1}}\left( {\frac{3}{5}} \right)$

b
(b)We have
$max\ amp(z)=amp$$({z_2}),$ $min\ amp (z)=amp$$({z_1})$
Now $amp({z_1}) = {\theta _1} = {\cos ^{ - 1}}\left( {\frac{{15}}{{25}}} \right) = {\cos ^{ - 1}}\left( {\frac{3}{5}} \right)$
$amp({z_2}) = \frac{\pi }{2} + {\theta _2} = \frac{\pi }{2} + {\sin ^{ - 1}}\left( {\frac{{15}}{{25}}} \right) = \frac{\pi }{2} + {\sin ^{ - 1}}\left( {\frac{3}{5}} \right)$
$|\max \,\,amp(z) - \min \,\,amp(z)|$
$ = \left| {\frac{\pi }{2} + {{\sin }^{ - 1}}\frac{3}{5} - {{\cos }^{ - 1}}\frac{3}{5}} \right|$
$ = \left| {\frac{\pi }{2} + \frac{\pi }{2} - {{\cos }^{ - 1}}\frac{3}{5} - {{\cos }^{ - 1}}\frac{3}{5}} \right| = \pi - 2{\cos ^{ - 1}}\frac{3}{5}$

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

Find the mean of the first five multiples of $7.$

Let $x_1, x_2, \ldots, x_{11}$ be 11 distinct positive integers. If we replace the largest of these integers by the median of the other $10$ integers, then

If the set of natural numbers is partitioned into subsets ${S_1} = \left\{ 1 \right\},\;{S_2} = \left\{ {2,\;3} \right\},\;{S_3} = \left\{ {4,\;5,\;6} \right\}$ and so on. Then the sum of the terms in ${S_{50}}$ is

$\lim _{n \rightarrow \infty}\left(1+\frac{1+\frac{1}{2}+\ldots \ldots .+\frac{1}{n}}{n^{2}}\right)^{n}=.........$

Let $a_1, a_2, \ldots . a_{10}$ be $10$ observations such that $\sum_{\mathrm{k}=1}^{10} \mathrm{a}_{\mathrm{k}}=50$ and $\sum_{\forall \mathrm{k}<\mathrm{j}} \mathrm{a}_{\mathrm{k}} \cdot \mathrm{a}_{\mathrm{j}}=1100$. Then the standard deviation of $a_1, a_2, \ldots, a_{10}$ is equal to :

$\frac{1}{\text{Z}}$ is, _________________ for complex number z.

For $x \in R$, then number of real roots of the equation $3 x^2-4\left|x^2-1\right|+x-1=0$ is. . . . . .

If the arithmetic mean of the numbers ${x_1},{x_2},{x_3},\,......,\,{x_n}$ is $\bar x$, then the arithmetic mean of numbers $a{x_1} + b,\,a{x_2} + b,\,a{x_3} + b,\,........,a{x_n} + b$, where $a, b$ are two constants would be

$\frac{{{{\sin }^3}\,\theta \,\, - \,\,{{\cos }^3}\,\theta }}{{\sin \,\theta \,\, - \,\,\cos \,\theta }} - \frac{{\cos \,\theta }}{{\sqrt {1\,\, + \,\,{{\cot }^2}\,\theta } }} - 2 \,tan \,\theta \,cot\, \theta = - 1$ if

$\text{f}(\text{x})={\frac{\text{|x|}}{\text{x}}}$ for $ \text{x} ≠ 0$ and $ 0$ for $ \text{x} = 0$ Which function is this?