The conjugate of a + 
is a − .
When a conjugate pair are multiplied, the form produced is The Difference of Two Squares.
(a + )(a − ) = a² − ()² = a² − b.
The conjugate of a + ib is a − ib,
where i is the complex unit: i² = −1.
When that conjugate pair are multiplied, we obtain the sum of the squares of the components a and b.
| (a + ib)(a − ib) | = | a² − (ib)² |
| = | a² − i²b² | |
| = | a² − (−1)b² | |
| = | a² + b² | |