If ${z_1}{\rm{ and }}{z_2}$ be complex numbers such that ${z_1} \ne {z_2}$ and $|{z_1}|\, = \,|{z_2}|$. If ${z_1}$ has positive real part and ${z_2}$ has negative imaginary part, then $\frac{{({z_1} + {z_2})}}{{({z_1} – {z_2})}}$may be

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

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

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

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 $|z|$ ?