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1) Evaluate \(|2\omega^2-4\omega-30|\) if \(\omega=1-5i.\)

2) Solve 2z + i = iz + 3. Express your answer in the form x + yi.

 Aug 10, 2019
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\(|2\omega^2-4\omega - 30| = \\ |2(1-5i)^2 -4(1-5i)-30| = \\ |2(1-10i-25)-4+20i-30|=\\ |-48 -20i - 34 + 20i|= 82\)

 

 

\(2z+i = iz + 3\\ (2-i)z = 3-i\\ z = \dfrac{3-i}{2-i} = \dfrac{(3-i)(2+i)}{5}=\dfrac 7 5 + i \dfrac 1 5\)

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 Aug 10, 2019
edited by Rom  Aug 10, 2019

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