If ${z_1}$ and ${z_2}$ are any two complex numbers then $|{z_1} + {z_2}{|^2}$ $ + |{z_1} - {z_2}{|^2}$ is equal to
$2|{z_1}{|^2}\,|{z_2}{|^2}$
$2|{z_1}{|^2} + \,2\,\,|{z_2}{|^2}$
$|{z_1}{|^2} + \,|{z_2}{|^2}$
$2|{z_1}|\,\,|{z_2}|$
The values of $z$for which $|z + i|\, = \,|z - i|$ are
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
If $z_1 , z_2$ and $z_3, z_4$ are $2$ pairs of complex conjugate numbers, then $\arg \left( {\frac{{{z_1}}}{{{z_4}}}} \right) + \arg \left( {\frac{{{z_2}}}{{{z_3}}}} \right)$ equals
If $\frac{3+i \sin \theta}{4-i \cos \theta}, \theta \in[0,2 \pi],$ is a real number, then an argument of $\sin \theta+\mathrm{i} \cos \theta$ is
If $z$ is a complex number such that $\frac{{z - 1}}{{z + 1}}$ is purely imaginary, then