conjugateComplex
ConjugateComplex refers to the complex conjugate of a complex number, or to a function that computes this conjugate in mathematical or programming contexts. If a complex number is written as z = a + bi, where a and b are real and i is the imaginary unit, then its complex conjugate is z̄ = a − bi. The operation leaves the real part unchanged and negates the imaginary part. For real numbers, z̄ = z; for purely imaginary numbers z = bi, z̄ = −bi.
- z z̄ = |z|^2, a nonnegative real number.
- (zw)̄ = z̄ w̄ and (z + w)̄ = z̄ + w̄.
In programming, a function named conjugateComplex typically returns the complex conjugate of its input. Representations vary:
- z = 3 + 4i yields z̄ = 3 − 4i.
Applications include simplifying division of complex numbers, computing Fourier and Laplace transforms, and contexts in physics