+15 Let $x$ and $y$ be complex numbers. If $x + y =2$ and $xy = 5$, then what is $x^2 + y^2$?
+129820 Let x = a + bi
Let y = c - bi
x + y = 2
a + c = 2
xy = (a + bi) (c - bi) =
ac + (c - a)bi + b^2 = 5
ac + 0bi + b^2 = 5
c- a = 0
c = a
a + c = 2
a + a = 2
2a = 2
a = 1 = c
ac + b^2 = 5
1*1 + b^2 = 5
1 + b^2 = 5
b^2 = 4
b = 2 or b = -2
( x + y)^2 = 2^2
x^2 + 2xy + y^2 = 4
x^2 + 2(5) + y^2 = 4
x^2 + y^2 = -6
