If $z = x + iy$ is a complex number and $|1 + iz| = |1 - iz|$, then

Let $z_1$ and $z_2$ be two complex numbers and roots of the equation $z^2 + az + b = 0$. If $O$ is the origin such that $OA = OB$ and $a^2 = \lambda b \cos^2 \frac{\alpha}{2}$,where $\alpha$ is the angle $\angle AOB$,then $\lambda$ is equal to:

If $z=x+iy$ satisfies the condition $|z+1|=1$,then $z$ lies on the

The locus of $z$ such that $\left|\frac{z-i}{z+i}\right|=2$,where $z=x+iy$,is

Let the minimum value $v_{0}$ of $v = |z|^{2} + |z-3|^{2} + |z-6i|^{2}$,where $z \in \mathbb{C}$,be attained at $z = z_{0}$. Then $|2z_{0}^{2} - \bar{z}_{0}^{3} + 3|^{2} + v_{0}^{2}$ is equal to:

Let $w_1$ be the point obtained by the rotation of $z_1=5+4i$ about the origin through a right angle in the anticlockwise direction,and $w_2$ be the point obtained by the rotation of $z_2=3+5i$ about the origin through a right angle in the clockwise direction. Then the principal argument of $w_1-w_2$ is equal to $...........$.