The equation $|z - i| = |z - 1|$,where $i = \sqrt{-1}$,represents:

Let $z_{1}$ and $z_{2}$ be two imaginary roots of $z^{2}+pz+q=0$,where $p$ and $q$ are real. The points $z_{1}, z_{2}$ and the origin form an equilateral triangle if

Let $R$ denote the set of all real numbers. Let $z_1 = 1 + 2i$ and $z_2 = 3i$ be two complex numbers,where $i = \sqrt{-1}$. Let $S = \{(x, y) \in R \times R : |x + iy - z_1| = 2|x + iy - z_2|\}$. Then which of the following statements is (are) True?
$(A) S$ is a circle with centre $\left(-\frac{1}{3}, \frac{10}{3}\right)$
$(B) S$ is a circle with centre $\left(\frac{1}{3}, \frac{8}{3}\right)$
$(C) S$ is a circle with radius $\frac{\sqrt{2}}{3}$
$(D) S$ is a circle with radius $\frac{2\sqrt{2}}{3}$

If $z_{1}$ and $z_{2}$ are two non-zero complex numbers such that $\frac{z_{1}}{z_{2}}+\frac{z_{2}}{z_{1}}=1$,then the origin and the points represented by $z_{1}$ and $z_{2}$:

If $z = x + iy$,then the area of the triangle whose vertices are the points $z$,$iz$,and $z + iz$ is

The locus of $z$ satisfying the inequality $\left|\frac{z+2 i}{2 z+i}\right| < 1$,where $z=x+i y$,is