powerplus (version 3.1)

explus: Scalar Exponentiation

Description

Raises any base (real or complex) to any power (even complex).

Usage

explus(a, numer, denom = 1, n.cycles = 10, tol = 1e-12)

Arguments

a

any base (real or complex). It can be a vector.

numer

numerator of exponent. Can be a decimal or complex number.

denom

denominator of exponent (1 by default). Can be a decimal or complex number.

n.cycles

The maximum number of steps to be used in the continued fraction approximation process done internally. Default is 10. Increasing this default may increase precision, but it may also produce unexpected results (even a runtime error).

tol

a tolerance, \(10^{-12}\) by default. Prevents possible numerical problems. Can be set to 0 if desired.

Value

The solution to the exponentiation operation supplied. Returns a real-valued root whenever possible. Otherwise, the principal complex root.

Details

Method based on numerical treatment of complex exponents using Euler Formula and angles measured in radians, which is the default method built-in in R.

References

For more on Euler Formula, visit http://mathworld.wolfram.com/EulerFormula.html

For more on complex exponents, visit http://mathworld.wolfram.com/ComplexExponentiation.html

Examples

explus(-3, 4, 2)
explus(-3, 2, 4)
explus(-3, 2, 3)
explus(-3, 5, 3)
explus(-3, 5, 2)
explus(-3, -2, 4)
explus(0-0.5773503i, 2)
explus(-0.4, pi)
explus(-0.37, 0.2)
explus(-0.37, 1, 5)
explus(5, 7i)
explus(2+3i, 1+2i)
explus(2+3i, 1+2i, -4+1i)
explus(2+3i, 1+2i, 8)