Find two complex numbers whose sum is 20 and whose product is 101.

Answer 1

Try working with

a + bi

a - bi

(a + bi) + (a - bi) = 20

2a = 20

a = 10

(10 + bi)(10 - bi) = 101

10² - b²i² = 101

100 + b² = 101

b = ±1

The complex numbers

10 + i

10 - i

satisfy the conditions. Test them.