OCR MEI FP1 2007 January — Question 8

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2007
SessionJanuary
TopicComplex Numbers Argand & Loci

8 It is given that \(m = - 4 + 2 \mathrm { j }\).
  1. Express \(\frac { 1 } { m }\) in the form \(a + b \mathrm { j }\).
  2. Express \(m\) in modulus-argument form.
  3. Represent the following loci on separate Argand diagrams.
    (A) \(\arg ( z - m ) = \frac { \pi } { 4 }\)
    (B) \(0 < \arg ( z - m ) < \frac { \pi } { 4 }\)