Complex Numbers and Complex Algebra: Conjugate of a Complex Number
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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. MATH.
2. MATH.                                                            8. MATH provided $z_{2} \neq 0$.
3. $\overline{z} = z$ if and only if $z$ is a real number.
4. MATH if $z = x+iy$.
5. MATH if $z = x+iy$.
6. MATH.

   
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