If complex numbers $z_1$, $z_2$ are such that $\left| {{z_1}} \right| = \sqrt 2 ,\left| {{z_2}} \right| = \sqrt 3$ and $\left| {{z_1} + {z_2}} \right| = \sqrt {5 – 2\sqrt 3 }$, then the value of $|Arg z_1 -Arg z_2|$ is

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 –

$arg\,(5 – \sqrt 3 i) = $

Let $a \neq b$ be two non-zero real numbers.Then the number of elements in the set $X =\left\{ z \in C : \operatorname{Re}\left(a z^2+ bz \right)= a \text { and }\operatorname{Re}\left(b z^2+ az \right)= b \right\}$ is equal to

Let $z,w$be complex numbers such that $\overline z + i\overline w = 0$and $arg\,\,zw = \pi $. Then arg z equals