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Let the numbers be x and y, then
x + y = 60 (which yields y = 60 - x)
xy = 1600 (replace y with 60 - x)
x(60 - x) = 1600
60x - x2 = 1600 (multiply by -1 to both sides)
x2 - 60x = -1600 (add 302 to both sides to complete the square)
x2 - 60x + 302 = -1600 + 900
(x - 30)2 = -700 (take the square root of both sides)
x - 30 = ± √-700 (add 30 to both sides and write -700 = (100)(7)(-1))
x = 30 ± (√100)(√7)(√-1)
x = 30 ± (10√7)i
So,
x = 30 + (10√7)i or x = 30 - (10√7)i
thus,
y = 60 - [30 + (10√7)i] or y = 60 - [30 - (10√7)i ]
y = 30 - (10√7)i or y = 30 + (10√7)i
Therefore,
[30 + (10√7)i] + [30 - (10√7)i] = 60
[30 + (10√7)i] [30 - (10√7)i] = 1600
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