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June 2016 p33 q9
1974
The complex numbers \(-1 + 3i\) and \(2 - i\) are denoted by \(u\) and \(v\) respectively. In an Argand diagram with origin \(O\), the points \(A, B\) and \(C\) represent the numbers \(u, v\) and \(u + v\) respectively.
- Sketch this diagram and state fully the geometrical relationship between \(OB\) and \(AC\).
- Find, in the form \(x + iy\), where \(x\) and \(y\) are real, the complex number \(\frac{u}{v}\).
- Prove that angle \(AOB = \frac{3}{4}\pi\).
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