For the complex number $z$, one from $z + \bar z$ and $z\,\bar z$ is

Let $z$ be complex number such that $\left|\frac{z-i}{z+2 i}\right|=1$ and $|z|=\frac{5}{2} \cdot$ Then the value of $|z+3 i|$ is 

Let $z_1$ and $z_2$ be two complex number such that $z_1$ $+z_2=5$ and $z_1^3+z_2^3=20+15 i$. Then $\left|z_1^4+z_2^4\right|$ equals-

Let $z$ and $w$ be the two non-zero complex numbers such that $|z|\, = \,|w|$ and $arg\,z + arg\,w = \pi $. Then $z$ is equal to

Find the modulus and argument of the complex numbers:

$\frac{1}{1+i}$

For any two complex numbers ${z_1},{z_2}$we have $|{z_1} + {z_2}{|^2} = $ $|{z_1}{|^2} + |{z_2}{|^2}$ then