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

If $|{z_1}|\, = \,|{z_2}|$ and $amp\,{z_1} + amp\,\,{z_2} = 0$, then

If $z = x + iy$ satisfies $|z|-2=0$ and $|z-i|-|z+5 i|=0$, then

Let $\bar{z}$ denote the complex conjugate of a complex number $z$. If $z$ is a non-zero complex number for which both real and imaginary parts of

$(\bar{z})^2+\frac{1}{z^2}$

are integers, then which of the following is/are possible value($s$) of $|z|$ ?

If $z = 3 + 5i,\,\,{\rm{then }}\,{z^3} + \bar z + 198 = $

If $|{z_1} + {z_2}| = |{z_1} - {z_2}|$, then the difference in the amplitudes of ${z_1}$ and ${z_2}$ is