1. If a > 0 and z|z| + az + 2a = 0 then z must be
a) purely imaginary
b) a positive real number
c) a negative real number
d) 0

Explanation:

2.If $\frac{3}{2+cos\theta+i\sin\theta}=a+ib$      , then $\left(a-2\right)^{2}+b^{2}$   equals
a) 0
b) 1
c) -1
d) 2

Explanation:

3. If $z=4+i\sqrt{7}$  , then value of $z^{3}-4z^{2}-9z+91$    equals
a) 0
b) 1
c) -1
d) 2

Explanation:

4. The number of complex number satisfying the equation |z| = 2 and |z| = |z – 1| is
a) 0
b) 1
c) 2
d) infinite

Explanation:

5. If $z=\frac{mz_{1}+z_{2}}{m+1}$   , then distance of point z from the line joining $z_{1}+1$  and $z_{2}+1$  is
a) 0
b) 1
c) $\frac{2m}{m+1}$
d) $\frac{m}{m+1}$

Explanation:

6. If $z_{1},z_{2},z_{3}$  are three complex number such that then $4z_{1}-7z_{2}+3z_{3}=0$     , then z1, z2, z3 are
a) vertices of a scalane triangle
b) vertices of a right triangle
c) points on a circle
d) collinear points

Explanation:

7. if a complex number z has modulus 1 and argument $\pi/3$   , then $z^{2}+z$
a) is purely imaginary
b) has modulus $\sqrt{3}$
c) lies on the imaginary axis
d) All of the Above

Explanation:

8. If $z_{1}=a+ib$   and $z_{2}=c+id$   numbers such that $\mid z_{1}\mid =\mid z_{2}\mid=1$    and Re $\left(z_{1}\bar{z}_{2}\right)=0$    , then the pair of complex numbers, $w_{1}=a+ic$    and $w_{2}=b+id$    satisfy
a) $\mid w_{1}\mid=1$
b) $\mid w_{2}\mid=1$
c) $\mid w_{1}\bar{w}_{2}\mid=1$
d) All of the Above

Explanation:

9. If $2\cos\theta=x+\frac{1}{x}$    and $2\cos\phi=y+\frac{1}{y}$    , then
a) $x^{n}+\frac{1}{x^{n}}=2\cos \left(n\theta\right)$
b) $\frac{x}{y}+\frac{y}{x}=2\cos \left(\theta-\phi\right)$
c) $xy+\frac{1}{xy}=2\cos \left(\theta+\phi\right)$
d) All of the Above

10. Number of real solutions of the equation $5\left(\sqrt{1+x}+\sqrt{1-x}\right)=6x+8\sqrt{1-x^{2}}$