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

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

Original: https://numbas.mathcentre.ac.uk/question/11788/arithmetics-of-complex-numbers-v/ by Newcastle University Mathematics and Statistics

Tramslated to German

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

Original: https://numbas.mathcentre.ac.uk/question/11784/arithmetics-of-complex-numbers-i/ by Newcastle University Mathematics ans Statistics

Translated to German.

Composite multiplication and division of complex numbers. Two parts.

Original: https://numbas.mathcentre.ac.uk/question/11787/arithmetics-of-complex-numbers-iv/ by Newcastle University Mathematics and Statistics

Translated to German

Inverse and division of complex numbers.  Four parts.

Original: https://numbas.mathcentre.ac.uk/question/11786/arithmetics-of-complex-numbers-iii/ by Newcastle University Mathematics and Statistics

Translated to German.

Multiplication and addition of complex numbers. Four parts.

Original: https://numbas.mathcentre.ac.uk/question/11785/arithmetics-of-complex-numbers-ii/ by Newcastle University Mathematics and Statistics

Translated to German.

Some simple multiple choice questions on the field of complex numbers.

Solve two quadratic equations (with real coefficients) in the complex numbers. The solutions have non-zero imaginary part, fractions can appear (but the denominators are rather small).

Solve two quadratic equations (with real coefficients) in the complex numbers. The solutions have non-zero imaginary part, fractions can appear (but the denominators are rather small).

Nature of fixed points of a 2D dynamical system.

These examples are either centres or spirals.

Self-assessment questions. Solve 50% of the available marks to pass this exercise.

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

Inverse and division of complex numbers.  Four parts.

Multiplication of complex numbers. Four parts.

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

Find the solution of a constant coefficient second order ordinary differential equation of the form $ay''+by=0$. Complex roots.

No description given

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. 

Find modulus and argument of two complex numbers.

Then use De Moivre's Theorem to find powers of the complex numbers.

AEP Y1 - Engineering Mathematics Assessment 1(i)

Note that part(i) counts 20% towards the final Y1 Engineering Mathematics module grade.

AEP Y1 - Engineering Mathematics Assessment 1(i)

Note that part(i) counts 20% towards the final Y1 Engineering Mathematics module grade.

AEP Y1 - Engineering Mathematics Assessment 1(i)

Note that part(i) counts 20% towards the final Y1 Engineering Mathematics module grade.

Practice to decide which quadrant a complex number lies in.

Practice to decide which quadrant a complex number lies in.

You are allowed 38 minutes to complete this test.

You may use rough paper for your calculations.

You are allowed 31 minutes to complete this test.

You may use rough paper for your calculations.

Two parts.

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

This complex numbers in-class assesment counts 20% towards your final maths grade for WM104.

Note that although questions are randomised for each student, all questions test the same learning outcomes at the same level for each student.  

If you have any questions during the test, please put up your hand to alert the invigilator that you need attention. 

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.