Complex Number Conjugate
Conjugate of a complex number
z is a complex number whose algebraic format is as follows,
`z = x + i * y`
Then, the conjugate of z, denoted by `bar z`, is defined by,
`bar z = x - i * y`
1) `z = 0 , bar z = 0`
2) `z = i , bar z = -i`
3) if z is a real number then `bar z = z`.
4) `z = 1+i , bar z = 1-i`.
1) The conjugate of the sum of two complex numbers is the sum of their conjugates.
`bar (y + z) = bar y + bar z`
2) The conjugate of the product of two complex numbers is the product of their conjugates.
`bar (y * z) = bar y * bar z`
3) The conjugate of a quotient of two complex numbers is the quotient of their conjugates.
`bar ((y / z)) = bar y / bar z`
4) `z*bar z = |z|^2`
5) A complex number and its conjugate have the same modulus.
`|bar z| = |z|`