Let $z_1 = 6 + i$ and $z_2 = 4 -3i$. Let $z$ be a complex number such that $arg\ \left( {\frac{{z – {z_1}}}{{{z_2} – z}}} \right) = \frac{\pi }{2}$, then $z$ satisfies –

If $z_1, z_2  $ are any two complex numbers, then $|{z_1} + \sqrt {z_1^2 – z_2^2} |$ $ + |{z_1} – \sqrt {z_1^2 – z_2^2} |$ is equal to

If ${z_1}$ and ${z_2}$ are two non-zero complex numbers such that $|{z_1} + {z_2}| = |{z_1}| + |{z_2}|,$then arg $({z_1}) – $arg $({z_2})$ is equal to

Let $z _{1}$ and $z _{2}$ be two complex numbers such that $\overline{ z }_{1}=i \overline{ z }_{2}$ and $\arg \left(\frac{ z _{1}}{\overline{ z }_{2}}\right)=\pi$. Then

Let $z$ =${i^{2i}}$ , then $|z|$ is (where $i$ =$\sqrt { – 1}$ )