Let $z$ be a complex number. Then the equation $z^4 + z + 2 = 0$ cannot have a root such that:

If $x-iy = \sqrt{\frac{a-ib}{c-id}}$,prove that $(x^2+y^2)^2 = \frac{a^2+b^2}{c^2+d^2}$.

If $z_1 = 1+2i$ and $z_2 = 3+5i$,then $\text{Re} \left( \frac{\bar{z}_2 z_1}{z_2} \right) = $

The Cartesian form of the complex number $z = 4(\cos 300^{\circ} + i \sin 300^{\circ})$ is

Let $z$ be a complex number such that $|z|-z=2+i$,where $i=\sqrt{-1}$. Then,$|z|=$

If $m_1, m_2, m_3$ and $m_4$ respectively denote the moduli of the complex numbers $1+4i, 3+i, 1-i$ and $2-3i$,then the correct relation among the following is: