The complex functions are those functions that:
The set of available double functions is:
| Function Name | Description | Notes |
|---|---|---|
| acsc | inverse cosecant | acsc(z) = asin(1.0 / z) |
| acsch | inverse hyperbolic cosecant | acsch(z) = asinh(1.0 / z) |
| acos | inverse cosine | acos(z) = -i * log(z + i * sqrt(1.0 - z * z)) |
| acosh | inverse hyperbolic cosine | acosh(z) = log(z + sqrt(z * z - 1.0)) |
| acot | inverse cotangent | acot(z) = atan(1.0 / z) |
| acoth | inverse hyperbolic cotangent | acoth(z) = atanh(1.0 / z) |
| asec | inverse secant | asec(z) = acos(1.0 / z) |
| asech | inverse hyperbolic cosecant | asech(z) = acosh(1.0 / z) |
| asin | inverse sin | asin(z) = -i * log(i * z + sqrt(1.0 - z * z)) |
| asinh | inverse hyperbolic sine | asinh(z) = log(z + sqrt(z * z + 1.0)) |
| atan | inverse tangent | result = tan(z), z = atan(result) |
| atanh | inverse hyperbolic tangent | atanh(value) = log((value + 1.0) / (value - 1.0)) / 2.0 |
| conj | complex conjugate | if z = [real, imaginary] then conj(z) = [real, -imaginary] |
| cos | cosine | cos(z) = (exp(i * z) + exp(-i * z)) / 2 |
| cosh | hyperbolic cosine | cosh(z) = (exp(z) + exp(-z)) / 2.0 |
| cot | cotangent | cot(z) = cos(z) / sin(z) |
| coth | hyperbolic cotangent | coth(z) = cosh(z) / sinh(z) |
| csc | cosecant | csc(z) = 1.0 / sin(z) |
| csch | hyperbolic cosecant | csch(z) = 1.0 / sinh(z) |
| exp | exponential | if z = [real, imaginary] then exp(z) = exp(real) * (cos(imaginary) + i * sin(imaginary)) |
| log | natural log |
for z = [real, imaginary], we can also express z in terms
of a distance 'r' and an angle 'theta'. log(z) = log(r) + i * theta. Log(z) is a multivalued function |
| sec | secant | sec(z) = 1.0 / cos(z) |
| sech | hyperbolic secant | sech(z) = 1.0 / cosh(z) |
| sin | sine | sin(z) = (exp(i * z) - exp(-i * z)) / 2.0 |
| sinh | hyperbolic sine | sinh(z) = (exp(z) - exp(-z)) / 2.0 |
| sqrt | square root |
The square root of z is the number that when multipled by itself is
equal to z. For example:
sqrt([0, 8]) == [2, 2] |
| tan | tangent | tan(z) = sin(z) / cos(z) |
| tanh | hyperbolic tangent | tanh(z) = sinh(z) / cosh(z) |
| Function Name | Description | Notes |
|---|---|---|
| pow | the power function | This function raises the first argument to the power of the second
argument
Here are some examples
pow([2, 2], [2, 0]) = [0, 8] This function can be used with a mixture of complex and real types as in:
pow([2, 2], 2) NOTE: You can also write pow(z1, z2) as "z1 ^ z2" |
| Function Name | Description | Notes |
|---|---|---|
| rotate | rotates a point a certain number of degrees around another point | As an example:
z = [2, 0]; This example says "rotate the point 'z' 90 degrees around the point [0, 0] (the origin)". In this case, the result will be [0, 2] |