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Question
What is the conjugate of `(sqrt(5 + 12i) + sqrt(5 - 12i))/(sqrt(5 + 12i) - sqrt(5 - 12i))`?
Solution
Let z = `(sqrt(5 + 12i) + sqrt(5 - 12i))/(sqrt(5 + 12i) - sqrt(5 - 12i)) xx (sqrt(5 + 12i) + sqrt(5 - 12i))/(sqrt(5 + 12i) + sqrt(5 - 12i))`
= `(5 + 12i + 5 - 12i + 2 sqrt(25 + 144))/(5 + 12i - 5 + 12i)`
= `3/(2i)`
= `(3i)/(-2)`
= `0 - 3/2 i`
Therefore, the conjugate of z = `0 + 3/2 i`.
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