If $|{z_1} + {z_2}| = |{z_1} - {z_2}|$, then the difference in the amplitudes of ${z_1}$ and ${z_2}$ is
$\frac{\pi }{4}$
$\frac{\pi }{3}$
$\frac{\pi }{2}$
$0$
If $z$ is a complex number such that $\left| z \right| \ge 2$ , then the minimum value of $\left| {z + \frac{1}{2}} \right|$:
The conjugate of the complex number $\frac{{2 + 5i}}{{4 - 3i}}$ is
If $z$ is a complex number, then the minimum value of $|z| + |z - 1|$ is
Let $S$ be the set of all complex numbers $z$ satisfying $\left|z^2+z+1\right|=1$. Then which of the following statements is/are $TRUE$?
$(A)$ $\left|z+\frac{1}{2}\right| \leq \frac{1}{2}$ for all $z \in S$ $(B)$ $|z| \leq 2$ for all $z \in S$
$(C)$ $\left|z+\frac{1}{2}\right| \geq \frac{1}{2}$ for all $z \in S$ $(D)$ The set $S$ has exactly four elements
The product of two complex numbers each of unit modulus is also a complex number, of