Mathematical skills - Complex numbers

Shows how to solve for cube roots, 4th roots and so on of complex numbers. Makes use of De Moivre's Theorem, but the focus is on a simple presentation style which shows why the result works.

A number of questions for students to test their understanding of the videos in this series followed by worked solutions.

Looks at the computation of square roots using complex number algebra. This uses simple problems to establish an approach to such problem solving which subsequently can be applied to more complex root problems.

Introduces the concepts of modulus and argument. Also spends some time showing how the modulus and argument of conjugates and inverses are related to the orginal complex number.

Introduces fast methods of complex number multiplication using the modulus/argument form. Spends sometime 'demonstrating' the vailidity of the result, although viewers could focus on just the result should they choose.

Shows how the rules for multiplication/division in modulus/argument form lead to a very useful interpretation of complex numbers as scaling and rotation operators. This is used to solve problems in many engineering scenarios. Obvious typo at 7min 30 where writing uses 110 instead of 100.

A rapid review of complex numbers as would be covered in introductory lectures. Thus definitions, the Argand diagram, simple multiplication, division and addition and complex conjugates.

Introduces fast methods of complex number division using the modulus/argument form. Spends sometime 'demonstrating' the vailidity of the result, although viewers could focus on just the result should they choose.

Introduces the exponential form for a complex number and demonstrates how this is consistent with the multiplication/division rules in modulus/argument form as well as interpretations as a scaling/rotation operator.