The number of integer solutions of the equation $|1-i|^x=2^x$ is

The real value of $\theta$ for which the expression $\frac{1 + i \cos \theta}{1 - 2i \cos \theta}$ is a real number is $(n \in I)$:

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

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

If $z_1, z_2$ are two complex numbers satisfying $\left|\frac{z_1-3 z_2}{3-z_1 \bar{z}_2}\right|=1$ and $\left|z_1\right| \neq 3$,then $\left|z_2\right|$ is equal to

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