Aspire Faculty ID #15271 · Topic: JAMIA MCA 2016 · Just now
JAMIA MCA 2016

The amplitude of $\dfrac{1+i\sqrt{3}}{\sqrt{3}+i}$ is equal to …

Solution

$\dfrac{1+i\sqrt{3}}{\sqrt{3}+i} = \dfrac{(1+i\sqrt{3})(\sqrt{3}-i)}{(\sqrt{3}+i)(\sqrt{3}-i)} = \dfrac{(\sqrt{3}+3)i + (\sqrt{3}-1)}{4}$. Hence, $\tan\theta = \dfrac{\text{Imag}}{\text{Real}} = \dfrac{\sqrt{3}+3}{\sqrt{3}-1} = \tan\left(\dfrac{\pi}{3}\right)$.
← Previous Next →

Previous 10 Questions — JAMIA MCA 2016

Nearest first
1
If $\cos^{2}\theta + \sec^{2}\theta = a$, then …
Topic: JAMIA MCA 2016
 2
If $\cos\theta + \cos^{3}\theta = \sin^{2}\theta$, then $\sin^{6}\theta - 4\sin^{4}\theta + 8\sin^{2}\theta$ is equal t…
Topic: JAMIA MCA 2016
 3
The value of $\tan1^{\circ} \cdot \tan2^{\circ} \cdot \tan3^{\circ} \cdots \tan89^{\circ}$ is …
Topic: JAMIA MCA 2016
 4
If $\cos\theta + \sec\theta = 3$, then $\cos^{2}\theta + \sec^{2}\theta$ is …
Topic: JAMIA MCA 2016
 5
The value of $2\sin^{2}\theta \cdot \cos^{2}\theta (\sec^{2}\theta + \csc^{2}\theta)$ is …
Topic: JAMIA MCA 2016
 6
$\displaystyle \int \sqrt{x}e^{\sqrt{x}}dx$ is equal to …
Topic: JAMIA MCA 2016
 7
$\displaystyle \int_{0}^{1}\frac{x}{(1-x)^{1/2}}dx$ is equal to …
Topic: JAMIA MCA 2016
 8
$\displaystyle \int_{0}^{\frac{\pi}{4}}\sec^{2}x\sin x\,dx=a+\sqrt{2}$, find $a$
Topic: JAMIA MCA 2016
 9
If $x>0$, then $\displaystyle \int |x|^{3} dx$ is equal to …
Topic: JAMIA MCA 2016
 10
$\displaystyle \int_{1}^{x}(1+\log t)^{2}\,dt$ is equal to …
Topic: JAMIA MCA 2016

Next 10 Questions — JAMIA MCA 2016

Ascending by ID
1
If $z$ be a complex number and $\bar{z}$ be its conjugate, then the number of solutions of $z^{2} + 2\bar{z} = 0$ is …
Topic: JAMIA MCA 2016
 2
If $z$ be a complex number, then one of the solutions of the equation $z^{2} + |z|^{2} = 0$ is …
Topic: JAMIA MCA 2016
 3
If $\omega$ is a cube root of unity, then the value of $(1 + \omega - \omega^{2})(1 - \omega + \omega^{2})$ is …
Topic: JAMIA MCA 2016
 4
Let cube roots of unity be $1, \omega, \omega^{2}$. Which of the following is a cube root of the equation $(x - 1)^{3} …
Topic: JAMIA MCA 2016
 5
If $m^{\text{th}}$ term of an A.P. is $n$ and $n^{\text{th}}$ term is $m$, then its $10^{\text{th}}$ term is …
Topic: JAMIA MCA 2016
 6
Let sum of $n$ terms of an A.P. be $S_n=3n^2+5$. If $T_n$ (the $n$th term) of this series is $159$, then $n$ is …
Topic: JAMIA MCA 2016
 7
If the roots of $x^3-9x^2+23x-15=0$ are in A.P., then their common difference is …
Topic: JAMIA MCA 2016
 8
If $\log_{2}(5\cdot2^{x}+1),\ \log_{4}(2^{\,1-x}+1)$ and $1$ are in A.P., then $x$ equals …
Topic: JAMIA MCA 2016
 9
If sum of $n$ terms of a series is $3n^2 + 4n$, then the series is …
Topic: JAMIA MCA 2016
 10
If ${}^8C_r - {}^7C_3 = {}^7C_2$, then $r$ is equal to …
Topic: JAMIA MCA 2016
Ask Your Question or Put Your Review.

loading...