complex_num v1.0.2 ComplexNum.Polar
Summary
Functions
Returns a Complex Number with the same magnitude as this one,
but with the imaginary part being 0
Retrieves the angle of the Complex number in Polar form
Divides a Complex Numbers in Polar form by another
Retrieves the magnitude of the Complex Number in Polar form
Computes the square of the magnitude of the Complex number in Polar Form
Multiplies two Complex Numbers in Polar form
Creates a new Complex Numbers in Polar Form
from the given magnitude
and angle
, which can be written as:
magnitude * e^{angle * i}
Integer exponentiation of a number in Polar form
Converts a Complex Number in Polar form to Cartesian form
Functions
Returns a Complex Number with the same magnitude as this one,
but with the imaginary part being 0
.
Retrieves the angle of the Complex number in Polar form.
For r * e^{i * angle}
this is angle
.
This is a precise operation. (In stark contrast to computing the magnitude on a Complex Number in Cartesian form!)
Divides a Complex Numbers in Polar form by another.
This is a precise and very fast operation:
(r1 * e^{i * angle1}) / (r2 * e^{i * angle2}) = (r1 / r2) * e^{i * (angle1 - angle2)}
Retrieves the magnitude of the Complex Number in Polar form.
For r * e^(i * angle)
this is r
This is a precise operation. (In stark contrast to computing the magnitude on a Complex Number in Cartesian form!)
Computes the square of the magnitude of the Complex number in Polar Form.
For r * e^(i * angle)
this is r²
Multiplies two Complex Numbers in Polar form.
This is a precise and very fast operation:
(r1 * e^{i * angle1}) * (r2 * e^{i * angle2}) = (r1 * r2) * e^{i * (angle1 + angle2)}
Creates a new Complex Numbers in Polar Form
from the given magnitude
and angle
, which can be written as:
magnitude * e^{angle * i}
Integer exponentiation of a number in Polar form.
This is a precise and very fast operation:
(r1 * e^{i * angle1}) ^ (r2 * e^{i * angle2}) = (r1^r2) * e^{i * (angle1 * angle2)}