Embibe Experts Solutions for Chapter: Complex Numbers, Exercise 2: EXERCISE-2

Let $z$ and $\omega$ are two complex numbers such that $\left|z\right|\le 1,\left|\omega \right|\le 1$ and $|z+i\omega |=|z-i\overline{\omega }|=2$, then $z$ equals:

Which of the following locus of z on the complex plane represents a pair of straight lines?

If the complex numbers $z_1,z_2,z_3$ represents vertices of an equilateral triangle such that $\left|z_1\right|=\left|z_2\right|=\left|z_3\right|$, then which of following is correct?

If $S$ be the set of real values of $x$ satisfying the inequality $1-{\log }_2\frac{|x+1+2i|-2}{\sqrt{2}-1}\ge 0$, then $S$ contains

If the vertices of an equilateral triangle are situated at $z=0,z=z_1,z=z_2$, then which of the following is/are true -

Value(s) of $(-i{)}^{\frac{1}{3}}$ is/are -

Centre of square $ABCD$ is at $z=0$. If affix of vertex $A$ is $z_1$, centroid of triangle $ABC$ can be:

If $\omega$ is an imaginary cube root of unity, then a root of equation $\left|\begin{array}{ccc}x+1& \omega & {\omega }^2\\ \omega & x+{\omega }^2& 1\\ {\omega }^2& 1& x+2\end{array}\right|=0$, can be