Find two complex numbers whose sum is 12 and whose product is 37.

6 ± i and 6 ± i

Step-by-step explanation:

Let x be the first number.

Let y be the second number.

x + y = 12

x * y = 37

Solve for x in the first equation.

x = 12 - y

Put x as 12-y in the second equation and solve for y.

(12 - y) y = 37

12y - y² = 37

- y² + 12y - 37 = 0

y = 6 ± i

Put y as 6 ± i in the first equation and solve for x.

x + 6 ± i = 12

x = 12 - 6 ± i

x = 6 ± i