Complex Computations, Exponential and Logarithmic Functions

Exponential Function: Exp(x) = {Exp(x.r)*Cos(x.i), Exp(x.r)*Sin(x.i)}
See: Exponential Function -- From MathWorld
and Wolfram Function Evaluation

Power Functions, x^y: Pow(x, y) = Exp(y * Ln(x)),
but not defined if x = 0 and y.r is <= 0,
except 0^0 = 1 and = 0 if x = 0 and y.r is > 0.
See: Power -- From MathWorld
and Wolfram Function Evaluation

Square: Sq(x) = x^2 = x*x
See: Square -- From MathWorld
and Wolfram Function Evaluation

Square Root, The positive Square Root function: SqRt(x) = x^(1/2) = Pow(x, 1/2)
Of the two roots, the one with its real part > 0 is taken,
but if the real part is zero, the one on the positive y-axis.
See: Square Root -- From MathWorld
and Wolfram Function Evaluation

Cube Root, CuRt(x) = x^(1/3) = Pow(x, 1/3)
Of the three roots, the one with the greater real part is taken,
but if x.i = 0 and x.r < 0, CuRt(x) = −Pow(|x.r|, 1/3).
See: Cube Root -- From MathWorld
and Wolfram Function Evaluation

Natural Logarithm, Log base e of x: Ln(x) = {Ln(x.r^2 + x.i^2) / 2, ATan2(x.i, x.r)},
but not defined for x = 0.
See: Natural Logarithm -- From MathWorld
and Wolfram Function Evaluation

Logarithm, Log base b of x: LogB(b, x) = Ln(x)/Ln(b),
but not defined for x = 0 or b = 0.
See: Logarithm -- From MathWorld
and Wolfram Function Evaluation

Common Logarithm, Log base 10 of x: Log(x) = LogB(10, x) = Ln(x)/Ln(10),
but not defined for x = 0.
See: Common Logarithm -- From MathWorld
and Wolfram Function Evaluation
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Changes last made on Wednesday, 15-Feb-06 20:51:56 PST

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