SOLUTION: The sum of two complex numbers is 6 and their product is 10. One number is? a. -3+i b. -3-i c. 3+i d. -6+i

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: The sum of two complex numbers is 6 and their product is 10. One number is? a. -3+i b. -3-i c. 3+i d. -6+i      Log On


   

Question 202880: The sum of two complex numbers is 6 and their product is 10. One number is?
a. -3+i
b. -3-i
c. 3+i
d. -6+i
Answer by dyakobovitch(40) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of two complex numbers is 6 and their product is 10. One number is?

a. -3+i
b. -3-i
***c. 3+i***
d. -6+i

We assume that we are dealing with a quadratic equation. The sum of two numbers is -b/a=6. Our product is c/a=10.

A quadratic equation is defined as Ax^2+Bx+C=0.

So, let's simply test our solutions to see which ones hold. We know that imaginary solutions for quadratics come in pairs or conjugates. By testing our answers, we see that C. 3+ i is the only answer to satisfy the solution.
3+i and 3-i. The sum is 6. The product is 10. C. We are done.

--
David