OCR MEI FP1 2007 June — Question 4

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2007
SessionJune
TopicComplex Numbers Arithmetic
TypeMultiplication and powers of complex numbers

4 Two complex numbers, \(\alpha\) and \(\beta\), are given by \(\alpha = 1 - 2 \mathrm { j }\) and \(\beta = - 2 - \mathrm { j }\).
  1. Represent \(\beta\) and its complex conjugate \(\beta ^ { * }\) on an Argand diagram.
  2. Express \(\alpha \beta\) in the form \(a + b \mathrm { j }\).
  3. Express \(\frac { \alpha + \beta } { \beta }\) in the form \(a + b \mathrm { j }\).