Find the complex numbers u = x + \mathrm{i}y such that x and y are real and u^2 = -15 + 8\mathrm{i}.
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Practise this questionf(x) = \cos^{-1}(\sin^{-1} x).[3 marks]\frac{\partial w}{\partial x} = -\frac{1}{9} at the point (4, y_0), calculate the value of y_0.[5 marks]\frac{\partial^2 w}{\partial y \partial x} - 2 \frac{\partial^2 w}{\partial y^2} = 0.[5 marks]z^2 - (3 + 2\mathrm{i})z + (5 + \mathrm{i}) = 0, for z.[5 marks]More practice: the rest of this paper · more Complex Numbers questions · all CAPE Pure Mathematics Unit 2 past papers