Topics:
Algebra, Calculus, Trigonometeric Equations, Complex numbers & Partial Derivatives

Students must complete the exam within 120 mins (standard time).

Questions have variables to produce randomised questions.

Topics:
Algebra, Calculus, Trigonometeric Equations, Complex numbers & Partial Derivatives

Students must complete the exam within 120 mins (standard time).

Questions have variables to produce randomised questions.

Topics:
Algebra, Calculus, Trigonometeric Equations, Complex numbers & Partial Derivatives

Students must complete the exam within 2hrs 30mins (extra time (1)).

Questions have variables to produce randomised questions.

Given two complex numbers, find by inspection the one that is a root of a given quartic real polynomial and hence find the other roots. 

Topics:
Algebra, Calculus, Trigonometeric Equations, Complex numbers & Partial Derivatives

Students must complete the exam within 120 mins (standard time).

Questions have variables to produce randomised questions.

Modulus and argument of a single complex number $z=z_1/z_2$, where $\mathrm{Re}(z_1)=\mathrm{Im}(z_1)$ and $\mathrm{Re}(z_2)=-\mathrm{Im}(z_2)$.

Calculation of modulus, argument, multiplication by complex conjugate, given two complex numbers.

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

Practice MCQ to decide which quadrant a complex number lies in.

Quiz covering basic arithmetic with complex numbers, solving a quadratic with complex solutions and converting to/from polar and rectangular forms.

No description given

Elementary examples of multiplication and addition of complex numbers. Four parts.

Multiplication and addition of complex numbers. Four parts.

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

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

Rearrange a complex formula involving squares, square roots, fractions and additions. This is a fixed question with no randomisation.

More difficult trigonometric equations with radians

Show one of several blocks of text depending on the value of a question variable.

As well as a simple check for the value of a variable, the condition to display a block of text can be a complex expression in any of the question variables - in this example, depending on the discriminant of the generated quadratic.

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.

Recovering original function given some information such as derivative and value at some point.

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!

Find modulus and argument of two complex numbers. Then use De Moivre's Theorem to find positive powers of the complex numbers.

Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.

Using a given list of four complex numbers, find by inspection the one that is a root of a given cubic real polynomial and hence find the other roots.

Given random graph of cirlce, write locus in complex form. centre in 1st quadrant

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