OCR
Further Pure Core 2
2018
December
— Question 1
Exam Board
OCR
Module
Further Pure Core 2 (Further Pure Core 2)
Year
2018
Session
December
Topic
Complex numbers 2
1
The Argand diagram below shows the two points which represent two complex numbers, \(z _ { 1 }\) and \(z _ { 2 }\).
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On the copy of the diagram in the Printed Answer Booklet
draw an appropriate shape to illustrate the geometrical effect of adding \(z _ { 1 }\) and \(z _ { 2 }\),
indicate with a cross \(( \times )\) the location of the point representing the complex number \(z _ { 1 } + z _ { 2 }\).
You are given that \(\arg z _ { 3 } = \frac { 1 } { 4 } \pi\) and \(\arg z _ { 4 } = \frac { 3 } { 8 } \pi\).
In each part, sketch and label the points representing the numbers \(z _ { 3 } , z _ { 4 }\) and \(z _ { 3 } z _ { 4 }\) on the diagram in the Printed Answer Booklet. You should join each point to the origin with a straight line.
(i) \(\left| z _ { 3 } \right| = 1.5\) and \(\left| z _ { 4 } \right| = 1.2\)
(ii) \(\left| z _ { 3 } \right| = 0.7\) and \(\left| z _ { 4 } \right| = 0.5\)