SOLUTION: REINFORCE Find two complex numbers that have a sum of 10i, a difference of -4, and a product of -29

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: REINFORCE Find two complex numbers that have a sum of 10i, a difference of -4, and a product of -29      Log On


   

Question 849597: REINFORCE Find two complex numbers that have a sum of 10i, a difference of -4, and a product of -29
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
%28a%2Bbi%29%2B%28c%2Bdi%29=10i would indicate that a=-c.

The variablized complex numbers may then be called a+bi and -a+di.

%28a%2Bbi%29-%28-a%2Bdi%29=-4
a%2Ba%2Bbi-di=-4
2a%2B%28b-d%29i=-4%2B0%2Ai
2a=-4 and b-d=0
highlight%28a=-2%29

EQUATIONS
-
b+d=10
-
b-d=0
-
Adding these for Elimination, 2b=10, so highlight%28b=5%29 and highlight%28d=5%29

The two numbers are a%2Bbi=highlight%28-2%2B5i%29 and -a%2Bdi=highlight%282%2B5i%29