Finding roots and real factors of z^n+k=0

The first resource guides your class through the process of using the real and complex roots of z^n+k=0 to write down its real factors.

The introduction includes the important result about the sum of conjugates and then uses equations of the form z^n=1 or z^n=-1 to establish that there is always an even number of complex roots, which can be put into conjugate pairs. It is then shown how each conjugate pair of roots produces a real quadratic factor, while each real root produces a real linear factor.

To practise all this there is an exercise with 7 questions for students to complete. Solutions to all the examples and the exercise are included.

The second resource contains an exercise with further examination-style questions on this topic. This could be used as additional practice in class or as a homework/test. Answers are provided.