Question bank/JEE Main/Mathematics

If
$\left| z_{1} + z_{2} \right|^{2} = \left| z_{1} \right|^{2} + \left| z_{z} \right|^{2}$
then which of the following is incorrect.

A$\frac{z_{1}}{z_{2}}$ is purely realB$\frac{z_{1}}{z_{2}}$ is purely imaginaryCamp [IMAGE] may be equal to [IMAGE]

Show answer and solution▾

$\left| z_{1} + z_{2} \right|^{2} = \left| z_{1} \right|^{2} + \left| z_{2} \right|^{2}$
So amp $\left( \frac{z_{1}}{z_{2}} \right)$ is may be $\frac{\pi}{2}$ 
or  $- \frac{\pi}{2}$

Source: Grass-G / M-18 Mathematics Paper 27 Nov Third.docx