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

Basic question on limit laws and the squeeze theorem for sequences.

Test whether a student knows the monotonic sequence theorem.

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

This exam covers 

• laws of indices
• using surds and rationalising the denominator
• expanding brackets
• simplifying expressions
• solving linear inequalities
• finding common factors
• dividing a polynomial with remainders, using algebraic division
• factor theorem
• remainder theorem
• inverse and composite functions

Questions about Pythagoras' theorem

Calculating complex numbers raised to an natural number exponent

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

Calculate the cube roots of a complex number using De Moivre.

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

Calculating complex numbers raised to an natural number exponent

Questions about Pythagoras' theorem

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

(Green’s theorem). $\Gamma$ a rectangle, find: $\displaystyle \oint_{\Gamma} \left(ax^2-by \right)\;dx+\left(cy^2+px\right)\;dy$.

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

(Green’s theorem). $\Gamma$ a rectangle, find: $\displaystyle \oint_{\Gamma} \left(ax^2-by \right)\;dx+\left(cy^2+px\right)\;dy$.

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Using Pythagoras' theorem to determine a non-hypotenuse side, where side lengths include surds and students enter using sqrt syntax

Using Pythagoras' theorem to determine the hypotenuse, where side lengths include surds and students enter using sqrt syntax

Pythagoras' Theorem and naming sides of right angled triangle

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Pythagoras Theorem, Trigonometric Ratios, radian and degrees, degrees to radians, Sine rule 

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Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

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.

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

Questions using Pythagoras' theorem involving integers and surds. 

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

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