Mathematics A, Further H235: Complex Numbers Topical Past Paper Questions
OCR AS Mathematics A, Further (H235) past-paper questions on Complex Numbers , free. This topic is frequently examined across 4 exam sessions. Sign in for the full topic-segregated question bank and AI worksheets.
Sample questions
In this question you must show detailed reasoning. You are given that a is a real root of the equation $ x^{4}+x^{3}+3x^{2}-5x=0 $. You are also given that $ a+2+3i $ is one root of the equation $$ z^{4}-2(1+a)z^{3}+(21a-10)z^{2}+(86-80a)z+(285a-195)=0. $$ Determine all possible…
(a) Solve the equation $ \omega + 2 + 7i = 3\omega^{*} - i $. [4] (b) Prove algebraically that, for non-zero z, $ z = -z^{*} $ if and only if z is purely imaginary. [2] (c) The complex numbers z and $ z^{*} $ are represented on an Argand diagram by the points A and B respectively…
In this question you must show detailed reasoning. (a) Solve the equation $ 2z^{2}-10z+25=0 $ giving your answers in the form $ a+bi $. [2] (b) Solve the equation $ 3\omega-2=\mathrm{i}(5+2\omega) $ giving your answer in the form $ a+bi $. [4]
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