If for complex numbers `z_1` and `z_2` and `|1-bar(z_1)z_2|^2-|z_1-z_2|^2=k(1-|z_1|^2)(1-|z_2|^2)` then `k` is equal to:

Explanation

Given `1−∣z_1​barz_2​∣^2+(−∣z_1bar​z_2​∣^2)=k(1−∣z_1​∣^2)(1−∣z_2​∣^2)`

⇒`1−∣z_1​∣^2∣z_2​∣^2−(∣z_1​∣^2+∣z_2​∣^2+2∣z_1​∣∣z_2​∣)`

=`k(1−∣z_1​∣^2−∣z_2​∣^2+∣z_1​∣^2∣z_2​∣^2)`

⇒`∣bar z_1​​∣^2=∣z_1​∣^2`

For k=2 the equation satisfy.

Hence, the answer is 2.