If the conjugate of $(x + iy)(1 - 2i)$ be $1 + i$, then
$x = \frac{1}{5}$
$y = \frac{3}{5}$
$x + iy = \frac{{1 - i}}{{1 - 2i}}$
$x - iy = \frac{{1 - i}}{{1 + 2i}}$
If $z_1 , z_2$ and $z_3, z_4$ are $2$ pairs of complex conjugate numbers, then $\arg \left( {\frac{{{z_1}}}{{{z_4}}}} \right) + \arg \left( {\frac{{{z_2}}}{{{z_3}}}} \right)$ equals
If $x+i y=\frac{a+i b}{a-i b},$ prove that $x^{2}+y^{2}=1$
If ${z_1},{z_2}$ and ${z_3},{z_4}$ are two pairs of conjugate complex numbers, then $arg\left( {\frac{{{z_1}}}{{{z_4}}}} \right) + arg\left( {\frac{{{z_2}}}{{{z_3}}}} \right)$ equals
If $z$ is a complex number satisfying $|z|^2 - |z| - 2 < 0$, then the value of $|z^2 + z sin \theta|$ , for all values of $\theta$ , is
The maximum value of $|z|$ where z satisfies the condition $\left| {z + \frac{2}{z}} \right| = 2$ is