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4 + 2i*sqrt(5) and 4 - 2i*sqrt(5)

[where i is the square root of -1]

Given a+b=8, we have b=8-a.

Given ab = 36, we can substitute b=8-a to get a(8-a) = 36, or

a2 - 8a + 36 = 0

Using the quadratic formula gives the two possible answers, which accounts for the fact that a and b can be switched without affecting the problem.

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