Let $z$ be a complex number. Then the angle between vectors $z$ and $ - iz$ is

Find the modulus and argument of the complex number $\frac{1+2 i}{1-3 i}$

If $z$ is a complex number, then the minimum value of $|z| + |z - 1|$ is

If ${z_1},{z_2} \in C$, then $amp\,\left( {\frac{{{{\rm{z}}_{\rm{1}}}}}{{{{{\rm{\bar z}}}_{\rm{2}}}}}} \right) = $

If complex numbers $z_1$, $z_2$ are such that $\left| {{z_1}} \right| = \sqrt 2 ,\left| {{z_2}} \right| = \sqrt 3$ and $\left| {{z_1} + {z_2}} \right| = \sqrt {5 - 2\sqrt 3 }$, then the value of $|Arg z_1 -Arg z_2|$ is

Let $z$ be a complex number with non-zero imaginary part. If $\frac{2+3 z+4 z^2}{2-3 z+4 z^2}$ is a real number, then the value of $|z|^2$ is. . . . .