The conjugate of the complex number $\frac{2 + 5i}{4 - 3i}$ is

If $2 + i$ is a root of the equation ${x^3} - 5{x^2} + 9x - 5 = 0$,then the other roots are

Find the modulus of $\frac{1+i}{1-i}-\frac{1-i}{1+i}$.

If ${z_1}, {z_2}, {z_3}$ are complex numbers such that $|{z_1}| = |{z_2}| = |{z_3}| = \left| \frac{1}{z_1} + \frac{1}{z_2} + \frac{1}{z_3} \right| = 1$,then $|{z_1} + {z_2} + {z_3}|$ is

If ${z_1}$ and ${z_2}$ are any two complex numbers,then $|{z_1} + {z_2}|^2 + |{z_1} - {z_2}|^2$ is equal to:

Let $z_1$ and $z_2$ be two complex numbers such that $z_1 + z_2$ and $z_1 z_2$ are both real. Then: