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 | |