Conjugate of a Complex Number: The complex conjugate , or simply, the conjugate of a complex number is denoted by and is defined by
Geometrically, the point is the reflection of the point on the real axis. Example: The conjugate of the complex number is the number . If then
Properties of Complex Conjugation:
1. if and only if . 7. . 2. . 8. provided . 3. if and only if is a real number. 4. if . 5. if . 6. .