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 $z = x + iy\, (x, y \in R,\, x \neq \, -1/2)$ , the number of values of $z$ satisfying ${\left| z \right|^n}\, = \,{z^2}{\left| z \right|^{n – 2}}\, + \,z{\left| z \right|^{n – 2}}\, + \,1\,.\,\left( {n \in N,n > 1} \right)$ is

If $z_{1}=2-i, z_{2}=1+i,$ find $\left|\frac{z_{1}+z_{2}+1}{z_{1}-z_{2}+1}\right|$

If $\frac{\pi }{2} < \alpha  < \frac{3}{2}\pi $ , then the modulus and argument of $(1 + cos\, 2\alpha ) + i\, sin\, 2\alpha $ is respectively

The solution of the equation $|z| – z = 1 + 2i$ is