SOLUTION: Find the real numbers (a) and (b) that satisfy this equation. (2+i)(a+ib)=11-2i I would appreciate if you could show the working out a swell :) Thank you in advance!

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find the real numbers (a) and (b) that satisfy this equation. (2+i)(a+ib)=11-2i I would appreciate if you could show the working out a swell :) Thank you in advance!       Log On


   

Question 917045: Find the real numbers (a) and (b) that satisfy this equation.
(2+i)(a+ib)=11-2i
I would appreciate if you could show the working out a swell :)
Thank you in advance!
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
(2+i)(a+ib)=11-2i
highlight%28-2i%29 then ai + 2bi = -2i, a+2b = -2
11 then 2a - b = 11
...
-2(a+ 2b = -2)
2a - b = 11
-5b = 15
b = -3 and a = 4 a+=+-2-2%28-3%29
and..checking
(2 + i)(4 - 3i) = 11 - 2i