Let $z$ be a complex number such that the real part of $\frac{z-2i}{z+2i}$ is zero. Then,the maximum value of $|z-(6+8i)|$ is equal to:

If the vertices $A, B$ and $C$ of an isosceles $\triangle ABC$ are respectively $z_1, z_2$ and $z_3$ and if $\angle C=90^{\circ}$,then

Let $z_{1}$ be a fixed point on the circle of radius $1$ centered at the origin in the Argand plane and $z_{1} \neq \pm 1$. Consider an equilateral triangle inscribed in the circle with $z_{1}, z_{2}, z_{3}$ as the vertices. Then, $z_{1} z_{2} z_{3}$ is equal to

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

The equation of any $Circle$ in the complex plane is of the form $z \bar{z} + b \bar{z} + \bar{b} z + c = 0$,where $b \in \mathbb{C}$ and $c \in \mathbb{R}$.

The values of $z$ for which $|z + i| = |z - i|$ are