52
MCQ (Single Correct Answer)
The complex number $z$ which satisfies the condition $\left|\frac{i+z}{i-z}\right|=1$ lies on
A
circle $x^2+y^2=1$
B
the $X$-axis
C
the $Y$-axis
D
the line $x+y=1$
53
MCQ (Single Correct Answer)
If $z$ is a complex number, then
A
$\left|z^2\right|>|z|$
B
$\left|z^2\right|=|z|^2$
C
$\left|z^2\right|<|z|^2$
D
$\left|z^2\right| \geq|z|^2$
54
MCQ (Single Correct Answer)
$\left|z_1+z_2\right|=\left|z_1\right|+\left|z_2\right|$ is possible, if
A
$z_2=\bar{z}_1$
B
$z_2=\frac{1}{z_1}$
C
$\arg \left(z_1\right)=\arg \left(z_2\right)$
D
$\left|z_1\right|=\left|z_2\right|$
55
MCQ (Single Correct Answer)
The real value of $\theta$ for which the expression $\frac{1+i \cos \theta}{1-2 i \cos \theta}$ is a real number is
A
$n \pi+\frac{\pi}{4}$
B
$n \pi+(-1)^n \frac{\pi}{4}$
C
$2 n \pi \pm \frac{\pi}{2}$
D
None of these
56
MCQ (Single Correct Answer)
The value of $\arg(x)$, when $x < 0$ is
A
0
B
$\frac{\pi}{2}$
C
$\pi$
D
None of these