Complex number

[Balaviswanth]

I can't understand the step which I saw in a video solution for the question where the change |z| into |-z|.I attached the question below.

 

[pka]

I can't understand the step which I saw in a video solution for the question where the change |z| into |-z|.I attached the question below.

I suggest that you post a link to that video. In the meantime.
It is true that \(\displaystyle |-z|=|z|,~z\cdot \overline{z}=|z|^2~\&~\frac{z_1}{z_2}=\frac{z_1\cdot\overline{z_2}}{|z_2|^2}\)
What does it take for \(\displaystyle \frac{z_1\cdot\overline{z_2}}{|z_2|^2}\) to be purely imaginary?

 

[Balaviswanth]

Thank you!!!! This is really very helpful for me.