Complex Computations, Components

Real part: Real(x) = x.r

Imaginary part: Imag(x) = x.i

Absolute value: Abs(x) = |x| = SqRt(x.r^2 + x.i^2)

Argument: Arg(x)= ATan2(x.i, x.r)

Complex Conjugate: Conj(x) = {x.r, −x.i}

Negative: −x = {−x.r, −x.i}

Sign: Sign(x) = 0 if x = 0, else Sign(x) = {x.r/|x|, x.i/|x|}
It is 0 or the unit vector in the same direction as x.

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