find two complex numbers who have a sum of 14 and a product of 74.

Question

isn't it 7+i and 7-i? i am so confused...

Answer 1

while they do add to 14 they do not multiply to 74

In order for two complex numbers to both add and multiply to whole numbers they must be a pair like this

a+bi // a-bi

you understood that a has to be 7 because it is half of 14

yet neglect to see that b can be anything, not just 1

if we multiply the two

(a+bi)(a-bi)

a^2- abi + abi -b^2i^2

a^2 +b^2 (note i^2 =-1)

and substitute 7 for a and set it equal to 74

7^2 + b^2 = 74

49 + b^2 = 74

b^2 = 25

b = 5

so the pair will be

7+5i and 7-5i