1. Let L be the straight line $\bar{a}z+a\bar{z}+c=0,a \neq0$      $c\epsilon R$  , and OA be the straight line joining O and A(a), then
a) $L\parallel OA$
b) $L\perp OA$
c) L makes an angle of $\pi/4$ with OA
d) none of these

Explanation:

2. Locus of point z so that z, i, and iz are collinear, is
a) a straight line
b) a circle
c) an ellipse
d) a rectangular hyperbola

Explanation:

3. The number of roots of the equation $\mid z^{2}\mid -5 \mid z\mid +1 =0$     is
a) 0
b) 2
c) 4
d) infinite

Explanation:

4.The set of points in C satisfying the inequality $\mid arg \left(z\right)-\pi/2\mid <\pi/2$     is given by
a) $\left\{z: Re \left(z\right)> 0\right\}$
b) $\left\{z: In \left(z\right)< 0\right\}$
c) $\left\{z: Im \left(z\right)> 0\right\}$
d) $\left\{z: Re \left(z\right)=Im \left(z\right)\right\}$

Explanation:

5.If n $\geq$ 3 and $1, \alpha_{1},\alpha_{2},...\alpha_{n-1}$     are nth roots of unity, then value of $\sum_{1\leq i < j \leq n-1}\alpha_{i}\alpha_{j}$     is
a) 0
b) 1
c) -1
d) $\left(-1\right)^{n}$

Explanation:

6. The Quadrilateral formed by the point with affix 0, z, z + iz and iz is
a) parallelogram
b) rhombus
c) rectangle
d) square

Explanation:

7. If |z – 2| = 2|z – 1|, then $3|z|^{2} -4 Re \left(z\right)$     equals
a) 0
b) -1
c) 1
d) none of these

Explanation:

8. Sum of the common roots of $z^{2006}+z^{100}+1=0$     and $z^{3}+2z^{2}+2z+1=0$     is
a) 0
b) -1
c) 1
d) 2

Explanation:

9. If $z_{1}$ and $z_{2}$ lie on the same side the line $\bar{a}z+a\bar{z}+b =0$    , where $a \epsilon C, a\neq 0,b\epsilon R$    , then the ratio $\frac{\bar{a}z_{1}+a\bar{z}_{1}+b }{\bar{a}z_{2}+a\bar{z}_{2}+b }$    is
a) purely imaginary
b) a positive real number
c) a negative real number
d) none of these

10.If $z_{1}$ and $z_{2}$ are the roots of the equation $z^{2}+az+b=0$   , then prove that the origin, $z_{1}$ and $z_{2}$ form an equilateral triangle if and only if
a) $a^{2}=3b$
b) $b^{2}=3a$
c) $a^{2}+3b=0$
d) $b^{2}+3a=0$