Finding the distance between two complex numbers using the modulus of their difference. Three parts.

Calculate a particular harmonic component of the complex form of a Fourier series expansion.

Direct calculation of low positive and negative powers of complex numbers. Calculations involving a complex conjugate. Powers of $i$. Four parts.

Questions about complex arithmetic; argument and modulus of complex numbers; complex roots of polynomials; de Moivre's theorem.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Several problems involving dividing fractions, with increasingly difficult examples, including mixed numbers and complex fractions. 

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Questions about complex arithmetic; argument and modulus of complex numbers; complex roots of polynomials; de Moivre's theorem.

Questions about complex arithmetic; argument and modulus of complex numbers; complex roots of polynomials; de Moivre's theorem.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Quiz covering basic arithmetic with complex numbers and solving roots for a quadratic with complex solutions

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Inverse and division of complex numbers.  Four parts.

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

Multiplication and addition of complex numbers. Four parts.

Multiplication and addition of complex numbers. Four parts.

Multiplication and addition of complex numbers. Four parts.

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

This question provides practice at adding, subtracting, dividing and multiplying complex numbers in rectangular form.

This question provides practice at adding, subtracting, dividing and multiplying complex numbers in rectangular form.

This exercise will help you rearrange some complex equations.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.