SOLUTION: Hi, I was wondering if someone could help me with this problem. Simplify the following by hand. Give the answer in the form a+bi (a, b are real). (2-i)/(5+i) Thanks, Judy

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Hi, I was wondering if someone could help me with this problem. Simplify the following by hand. Give the answer in the form a+bi (a, b are real). (2-i)/(5+i) Thanks, Judy      Log On


   

Question 216176: Hi, I was wondering if someone could help me with this problem.
Simplify the following by hand. Give the answer in the form a+bi (a, b are real).
(2-i)/(5+i)
Thanks, Judy
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify the following by hand. Give the answer in the form a+bi (a, b are real).
%28%282-i%29%29%2F%28%285%2Bi%29%29
Multiply the equation by the conjugate of the denominator over itself
%28%282-i%29%29%2F%28%285%2Bi%29%29 * %28%285-i%29%29%2F%28%285-i%29%29
FOIL and combine like terms
%2810+-+2i+-+5i+%2B+i%5E2%29%2F%2825+-+5i+%2B+5i+%2B+i%5E2%29 = %2810+-+7i+%2B+i%5E2%29%2F%2825+-+i%5E2%29
remember i^2 = -1
%2810+-+7i+%2B+%28-1%29%29%2F%2825+-+%28-1%29%29 = %2810+-+7i+-+1%29%2F%2825+%2B+1%29 = %289+-+7i%29%2F26 0r 9%2F26 - %287i%29%2F26