5 marksComplex Numbers
CAPE Pure Mathematics Unit 2 · May/June 2012 · Paper 2 · Question 6(b)(ii)
Hence, find ALL complex roots of the equation z^2 - (3 + 5i)z - (4 - 7i) = 0.
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Practise this questionOther parts of this question
- 6(a)(i)Draw the points
AandBon an Argand diagram.[6 marks] - 6(a)(ii)Hence, or otherwise, show that the argument of
\frac{(1 + \sqrt{2} + i)}{1 - i}is EXACTLY\frac{3\pi}{8}.[5 marks] - 6(b)(i)Find ALL complex numbers,
z, such thatz^2 = i.[3 marks] - 6(c)Use de Moivre's theorem to show that
\cos 6\theta = \cos^6 \theta - 15\cos^4 \theta \sin^2 \theta + 15\cos^2 \theta \sin^4 \theta - \sin^6 \theta.[6 marks]
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