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
$-2$
48
MCQ (Single Correct Answer)
Which of the following is correct for any two complex numbers $z_1$ and $z_2$ ?
A
$\left|z_1 z_2\right|=\left|z_1\right|\left|z_2\right|$
B
$\arg \left(z_1 z_2\right)=\arg \left(z_1\right) \cdot \arg \left(z_2\right)$
C
$\left|z_1+z_2\right|=\left|z_1\right|+\left|z_2\right|$
D
$\left|z_1+z_2\right| \geq\left|z_1\right|-\left|z_2\right|$
49
MCQ (Single Correct Answer)
The point represented by the complex number $(2-i)$ is rotated about origin through an angle $\frac{\pi}{2}$ in the clockwise direction, the new position of point is
A
$1+2 i$
B
$-1-2 i$
C
$2+i$
D
$-1+2 i$
50
MCQ (Single Correct Answer)
If $x, y \in R$, then $x+i y$ is a non-real complex number, if
A
$x=0$
B
$y=0$
C
$x \neq 0$
D
$y \neq 0$
51
MCQ (Single Correct Answer)
If $a+i b=c+i d$, then
A
$a^2+c^2=0$
B
$b^2+c^2=0$
C
$b^2+d^2=0$
D
$a^2+b^2=c^2+d^2$