Brahmagupta-Fibonacci Identity/Proof 4

Proof
Let $z_1 = a - b i, z_2 = c + d i$ be complex numbers.

Let $\cmod z$ denote the complex modulus of a given complex number $z \in \C$.

By definition of complex multiplication:


 * $(1): \quad z_1 z_2 = \paren {a c + b d} + \paren {a d - b c} i$

Then: