42
MCQ (Single Correct Answer)
$\sin x+i \cos 2 x$ and $\cos x-i \sin 2 x$ are conjugate to each other for
A
$x=n \pi$
B
$x=\left(n+\frac{1}{2}\right) \frac{\pi}{2}$
C
$x=0$
D
No value of $x$
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
$x=4 n+1$