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Question
What is the conjugate of `(2 - i)/(1 - 2i)^2`?
Solution
Given that z = `(2 - i)/(1 - 2i)^2`
= `(2 - i)/(1 + 4i^2 - 4i)`
= `(2 - i)/(1 - 4 - 4i)`
= `(2 - i)/(-3 - 4i)`
= `(2 - i)/(-3 - 4i) xx (-3 + 4i)/(-3 + 4i)`
= `(-6 + 8i + 3i - 4i^2)/((-3)^2 - (4i)^2)`
= `(-6 + 11i + 4)/(9 - 16i^2)`
= `(-2 + 11i)/(9 + 16)`
= `(-2 + 11i)/25`
= `(-2)/25 + 11/25 i`
∴ `barz = (-2)/25 - 11/25 i`
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