For any two complex numbers `z_1\ a n d\ z_2` and any two real numbers `a ,\ b` find the value of `|a z_1-b z_2|^2+|a z_2+b z_1|^2dot`

Explanation

` |a z_{1}-b z_{2}|^{2}+|b z_{1}+a z_{2}|^{2} `


`= [a^{2}|z_{1}|^{2}+b^{2}|z_{2}|^{2}-2 a b Re(z_{1} bar{z}_{2})]
+[b^{2}|z_{1}|^{2}+a^{2}|z_{2}|^{2}+2 a b Re(z_{1} bar{z}_{2})] `


`=(a^{2}+b^{2})(|z_{1}|^{2}+|z_{2}|^{2}) `