1. Tardigrade
  2. Question
  3. Mathematics
  4. If z1 and z2 are any two complex numbers then |z1+z2|2+|z1-z2|2 is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $z_1$ and $z_2$ are any two complex numbers then $\left|z_1+z_2\right|^2+\left|z_1-z_2\right|^2$ is equal to

Complex Numbers and Quadratic Equations

Solution:

$\left|z_1+z_2\right|^2+\left|z_1-z_2\right|^2$
$=\left|z_1\right|^2+\left|z_2\right|^2+z_1 \bar{z}_2+\bar{z}_1 z_2+\left|z_1\right|^2+\left|z_2\right|^2-z_1 \bar{z}_2-\bar{z}_1 z_2$
$=z\left(\left|z_1\right|^2+\left|z_2\right|^2\right)$