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Exam-Style Questions.Problems adapted from questions set for previous Mathematics exams. |
1. | IB Analysis and Approaches |
Consider \( w = a - bi \) where \( |w| = 1 \)
Show that \( \text{Re} \left( \frac{w + i}{w - i} \right) \) is always equal to 0.
2. | IB Analysis and Approaches |
Consider the complex numbers \(z_1 = c + 3i\) and \(z_2 = c^2-2-ci\)
(a) Find an expression for \(z_1z_2 \) in terms of \(c\).
(b) Hence, given that arg(\(z_1z_2 \)) = \( \tan^{-1} 2 \) show that:
$$c^3 - c^2 + c + 3 = 0 $$If you would like space on the right of the question to write out the solution try this Thinning Feature. It will collapse the text into the left half of your screen but large diagrams will remain unchanged.
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