43
MCQ (Single Correct Answer)
The real value of $\alpha$ for which the expression $\frac{1-i \sin \alpha}{1+2 i \sin \alpha}$ is purely real is
where, $n\in N$
A
$(n+1) \frac{\pi}{2}$
B
$(2 n+1) \frac{\pi}{2}$
C
$n \pi$
D
None of these
44
MCQ (Single Correct Answer)
If $z=x+i y$ lies in the third quadrant, then $\frac{\bar{z}}{z}$ also lies in the third quadrant, if
A
$x>y>0$
B
$x< y<0$
C
$y< x<0$
D
$y>x>0$
45
MCQ (Single Correct Answer)
The value of $(z+3)(\bar{z}+3)$ is equivalent to
A
$|z+3|^2$
B
$|z-3|$
C
$z^2+3$
D
None of these
46
MCQ (Single Correct Answer)
If $\left(\frac{1+i}{1-i}\right)^x=1$, then where, $n \in N$
A
$x=2 n+1$
B
$x=4 n$
C
$x=2 n$
D
$x=4 n+1$
47
MCQ (Single Correct Answer)
A real value of $x$ satisfies the equation $\left(\frac{3-4 i x}{3+4 i x}\right)=\alpha-i \beta(\alpha, \beta \in R)$, if $\alpha^2+\beta^2$ is equal to
A
1
B
$-1$
C
2
D
$-2$