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Complex numbers
Reading time: 1minThis section provides a set of commands dedicated to working with complex numbers. You can define complex numbers, perform operations to extract their components, convert between different forms, and manipulate them for various mathematical problems. These tools are essential for creating problems in algebra, advanced geometry, and other fields requiring complex number manipulation.
Example classroom uses
- Generate a random complex number and ask students to find its argument or express it in polar form.
- Provide a complex expression and ask students to determine its conjugate.
- Create a complex number or a polynomial with complex coefficients and challenge students to identify its real or imaginary parts.
👉Need concrete examples? Check out the Examples section to see how these functions are used in real exercises. It’s a great place to see how to combine random value generation, conditions, and solution logic in context.
Functions
argument
Given a complex number, computes the argument.
argument(Complex)conjugate
Given a complex number or expression, returns the conjugate.
conjugate(Complex)
conjugate(Polynomial)Given a complex number z or a polynomial with complex coefficients, returns its conjugate.
imaginary_part
Given a complex number or a polynomial, returns the imaginary part.
imaginary_part(Complex)
imaginary_part(Polynomial)Given a complex number z or a polynomial with complex coefficients, returns its imaginary part.
polar
Given a complex number in its binomial expression, converts it in its polar expression, or vice versa.
polar(Complex)
polar(Polynomial, Real)Given a complex number z , returns a list: the first element is the radius and the second one is the argument.
Given two reals r and θ, the radius and argument of a complex number, writes it in binomial form.
real_part
Given a complex number or a polynomial, returns the real part.
real_part(Complex)
real_part(Polynomial)Given a complex number z or a polynomial with complex coefficients, returns its real part.