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                        Complex numbers

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                        This 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 + bi is a - 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.

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                        Complex numbers

                        Function Reference argument conjugate imaginary_part polar real_part

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