Argconjugatez1z
Argconjugatez1z is a term used in some mathematical contexts to denote the argument (angle) of the complex conjugate of the product of two complex numbers, z1 and z. It is not a standard or universally adopted operator in mainstream complex analysis, but it appears in certain notes, software documentation, or niche expositions as a compact way to express a specific phase computation.
Let z1 and z be nonzero complex numbers. Write z1 = r1 e^{iθ1} and z = r e^{iθ2}, with
- Argconjugatez1z depends only on the arguments of z1 and z, not on their magnitudes.
- It equals the negative of the sum of the individual arguments, up to the chosen branch/wrapping
- If either z1 or z is zero, Argconjugatez1z is undefined due to the undefined argument of zero.
If z1 = e^{iα} and z = e^{iβ}, then Argconjugatez1z = -(α + β). If z1 and z have arguments 2 and