Complex numbers having the same real part and imaginary parts of opposite signs in a complex pair is defined as complex conjugates.
Conjugate of a complex number is denoted by `bar z` or z*. Let z be a complex number, z = a + ib, here, a and b are real numbers and i = `sqrt(-1)` .
The conjugate of z is,
`bar z` = a - ib.
For example, 5 + i and 5 - i are complex conjugates.
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There are several properties under complex conjugate learning, some of the properties of complex conjugate learning are as follows,
`bar(z + w)` = `barz` + `barw`
`bar(z w)` = `barz` `barw`
`barz` = z, if and only if z is real.
`bar(z^n)` = `(barz)^n` for any integer n.
`bar(|z|)` = |z|
|z|2 = z( `barz` ) = ( `barz` )z
`bar(barz)` = z (i.e., the conjugate of the conjugate of a complex number z is again that number)
z-1 = `barz / |z|^2` , if z is non-zero.
Below are the examples on complex conjugates -
|More topics in Complex Conjugates|
|Complex Conjugate Theorem|
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