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Complex numbers
Reading time: 1minThis section describes functions for working with complex numbers. These functions allow you to compute properties of complex numbers, extract their components, convert between representations, and manipulate them within mathematical expressions.
They are commonly used when generating exercises in algebra, advanced geometry, and other mathematical contexts involving complex numbers.
Tip: For practical examples showing how these functions are used when generating exercises, see the Examples section.
Function Reference
argument
Description
Computes the argument (angle) of a complex number.
Syntax
argument(Complex)Returns
The argument of the complex number, typically expressed in radians.
conjugate
Description
Returns the complex conjugate of a number or expression.
Syntax
conjugate(Complex)
conjugate(Polynomial)Returns
The conjugate of the input complex number or polynomial with complex coefficients.
Notes
- The conjugate of a complex number
a + biisa - bi.
imaginary_part
Description
Returns the imaginary component of a complex number or polynomial.
Syntax
imaginary_part(Complex)
imaginary_part(Polynomial)Returns
The imaginary part of the complex number or polynomial with complex coefficients.
polar
Description
Converts between binomial and polar representations of a complex number.
Syntax
polar(Complex)
polar(Real, Real)Returns
When given a complex number, returns a list containing:
- the modulus (radius)
- the argument (angle)
When given a radius r and argument θ, returns the corresponding complex number in binomial form.
Notes
- The returned list follows the format
[radius, argument].
real_part
Description
Returns the real component of a complex number or polynomial.
Syntax
real_part(Complex)
real_part(Polynomial)Returns
The real part of the complex number or polynomial with complex coefficients.