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Multiplying a complex number by its conjugate

In the same way that multiplying a bracket involving a surd by the conjugate of the bracket will produce a rational number, the same is try for multiplying a complex number by the complex conjugate.

Multiplying a complex number by its conjugate will always result in a real number.

Proof

Section titled “Proof”
  • Let . and are real.
  • and are real, so is real.

Example: find such that

Section titled “Example: find such that ”
  • Let
  • ,
  • ,