Really stuck on the following question (Q15 FP1 p64)
Given that λ ∈ ℝ and that z and w are complex numbers, solve the simultaneous equations z - iw = 2, z - λw = 1 - λ^2, giving your answers in the form a + ib, where a, b ∈ ℝ, and a and b are functions of λ.
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I got up to:
w = (i(-1-λ^2) + λ(-1-λ^2)) / -1-λ^2
w = i + λ
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the answer is 1 + iλ
where've I gone wrong!?
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For the next question, I'm given that 5-2i is a root of z^2 - 10z + c =0. How to approach this? I know that z - 5 + 2i will be a factor.