ComplexTrigonometricX extension - complex library

A collection for trigonometric for Complex

Sine

Compute the sine of this complex number.

Implements the formula:

sin(a + bi) = sin(a)cosh(b) - cos(a)sinh(b)i

where the (real) functions on the right-hand side are math.sin, math.cos, fastmath.cosh and fastmath.sinh.

Returns nan if either real or imaginary part of the input argument is NaN.

Infinite values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.

Examples:

sin(1 ± INFINITY i) = 1 ± INFINITY i
sin(±INFINITY + i) = NaN + NaN i
sin(±INFINITY ± INFINITY i) = NaN + NaN i

Compute the cosine of this complex number.

Implements the formula:

cos(a + bi) = cos(a)cosh(b) - sin(a)sinh(b)i

where the (real) functions on the right-hand side are math.sin, math.cos, fastmath.cosh and fastmath.sinh.

Returns nan if either real or imaginary part of the input argument is NaN.

Infinite values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.

Examples:

cos(1 ± INFINITY i) = 1 ∓ INFINITY i
cos(±INFINITY + i) = NaN + NaN i
cos(±INFINITY ± INFINITY i) = NaN + NaN i

Compute the tangent of this complex number.

Implements the formula:

tan(a + bi) = sin(2a)/(cos(2a)+cosh(2b)) + [sinh(2b)/(cos(2a)+cosh(2b))]i

where the (real) functions on the right-hand side are math.sin, math.cos, fastmath.cosh and fastmath.sinh.

Returns nan if either real or imaginary part of the input argument is NaN.

Infinite (or critical) values in real or imaginary parts of the input may result in infinite or NaN values returned in parts of the result.

Examples:

tan(a ± INFINITY i) = 0 ± i
tan(±INFINITY + bi) = NaN + NaN i
tan(±INFINITY ± INFINITY i) = NaN + NaN i
tan(±π/2 + 0 i) = ±INFINITY + NaN i

Compute the inverse sine of this complex number.

Implements the formula:

asin(z) = -i (log(sqrt(1 - z^2) + iz))

Returns nan if either real or imaginary part of the input argument is NaN or infinite.

Compute the inverse cosine of this complex number.

Implements the formula:

acos(z) = -i (log(z + i (sqrt(1 - z^2))))

Returns nan if either real or imaginary part of the input argument is NaN or infinite.

Compute the inverse tangent of this complex number.

Implements the formula:

atan(z) = (i/2) log((i + z)/(i - z))

Returns nan if either real or imaginary part of the input argument is NaN or infinite.