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Solve a conjugate equation without assuming conjugate roots

Do not use a calculator. One root of zz∗+2iz=a+6izz^*+2iz=a+6i, with a∈Ra\in\mathbb R, is z=3−7iz=3-7i. Find aa and the other root. marks

[2020/RI/Promo/7(a)]

CJC · Review problems · Question 16

The product zz* is x²+y². Compare the imaginary part before solving the real quadratic.

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