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

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

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

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.

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

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

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

Calculating complex numbers raised to an natural number exponent

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.

Composite multiplication and division of complex numbers. Two parts.

Inverse and division of complex numbers.  Four parts.

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

Multiplication and addition of complex numbers. Four parts.

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

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

Find the modulus and argument of complex numbers.

Content: complex arithmetic; argument and modulus of complex numbers; de Moivre's theorem.

This homework counts 10% towards your final Engineering Mathematics mark.

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

Polar form of a complex number.

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

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

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

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.

Find $\displaystyle I=\int \frac{2 a x + b} {a x ^ 2 + b x + c}\;dx$ by substitution or otherwise.

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. 

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.

Inverse and division of complex numbers.  Four parts.

Multiplication and addition of complex numbers. Four parts.

Multiplication and addition of complex numbers. Four parts.