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OPERATORS.md

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j = sqrt(-1)

Z = re + im*j

List of available operators in Complex_Functions.inc:

Re(Z) = re

Im(Z) = im

Id(Z) = Z

Pos(Z) = +Z

Neg(Z) = -Z

Conj(Z) = re - im*j

Abs(Z) = |Z| = sqrt(Z*conj(Z))

Phase(Z) = atan2(im, re)

Ln(Z) = ln(abs(Z)) + phase(Z)*j

Exp(Z) = e^Z

Sqr(Z) = Z^2

Sqrt(Z) = Z^0.5

Inv(Z) = 1/Z

Cos(Z) = (e^(-Z*j) + e^(+Z*j))/2

Acos(Z) = -ln(Z + sqrt(1 - Z^2)*j)*j

Sin(Z) = (e^(-Z*j) - e^(+Z*j))/2*j

Asin(Z) = -ln(sqrt(1 - Z^2) + Z*j)*j

Tan(Z) = sin(Z)/cos(Z)

Atan(z) = (ln(1 - Z*j) - ln(1 + Z*j))/2*j

Cosh(Z) = (e^(+Z) + e^(-Z))/2

Acosh(Z) = +ln(Z + sqrt(Z + 1)*sqrt(Z - 1))

Sinh(Z) = (e^(+Z) - e^(-Z))/2

Asinh(Z) = +ln(Z + sqrt(Z^2 + 1))

Tanh(Z) = sinh(Z)/cosh(Z)

Atanh(Z) = (ln(1 + Z) - ln(1 - Z))/2

Add(Z1, Z2) = Z1 + Z2

Sub(Z1, Z2) = Z1 - Z2

Mul(Z1, Z2) = Z1*Z2

Div(Z1, Z2) = Z1/Z2

Pow(Z1, Z2) = Z1^Z2