Question

Two complex numbers have a sum of 14 and a product of 74. Write either of the two numbers.

Answer 1

Hello,

Explanation:

The 2 numbers are roots of the equation:

U²-14U+74=0

Discriminant=14²-4*74=-100

U=7-5i or U=7+5i

Answer 2

9514 1404 393

Answer:

7 +5i or 7 -5i

Explanation:

If the two numbers are represented by x and y, then ...

x+y = 14

xy = 74

Substituting for y, we have ...

x(14 -x) = 74

x^2 -14x +49 = -74 +49 . . . . . multiply by -1, complete the square

(x -7)^2 = -25 . . . . . . . . . . . write as a square

x -7 = ±√(-25) = ±5i . . . . take the square root

x = 7 ± 5i . . . . . . . . . . . add 7

One of the numbers is 7 +5i.