Topics: Trigonometeric equations and complex numbers
Students must complete the exam within 90 mins (standard time).
Questions have variables to produce randomised questions.

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

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

Inverse and division of complex numbers.  Four parts.

Multiplication and addition of complex numbers. Four parts.

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

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.

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

A simple exercise requiring the calculation of the modulus and argument of complex numbers.

Inverse and division of complex numbers.  Four parts.

Division (Rationalising) complex numbers in rectangular (Cartesian) Form.

Thanks are due to Christian for his Gap Fills in Fractions code and method

Polar form of a complex number.

Practice to decide which quadrant a complex number lies in.

Complex number multiplication & division

modulus & argument of a complex number

Calculating the square root of a complex number using De Moivre.

Calculating complex numbers raised to an natural number exponent

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

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

given equation of locus in form |z-a|=bfind centre and radius. multiple choice question

given random circle on graph with centre in 2nd or 3rd quadrant. find loci in complex form

Given |z-a|=b multiple choice question to describe the locus

Simple multiplication of complex conjugates. Complex numbers are of the form $a+bi$ where $a$ and $b$ are randomised between 1 and 9 inclusive. 

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