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1) The complex numbers a and b satisfy $$a \overline{b} = -1 + 5i.$$

Find $$\overline{a} b.$$

2) Suppose z is a complex number such that z^2 = 24-32i. Find |z|.

3) Let f(x) = x^3 + 6x^2 + 16x + 28.The graphs of y = f(x) and y = f^{-1}(x) intersect at exactly one point (a,b). Enter the ordered pair (a,b).

Apr 13, 2019