SOLUTION: Find the quotient and enter the real and imaginary parts below. (5+8i)/(3+5i) it should look something like _=_i thank you!

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find the quotient and enter the real and imaginary parts below. (5+8i)/(3+5i) it should look something like _=_i thank you!      Log On


   



Question 834066: Find the quotient and enter the real and imaginary parts below.
(5+8i)/(3+5i)
it should look something like _=_i
thank you!

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
%285%2B8i%29%2F%283%2B5i%29

The conjugate of the denominator is 3-5i.  Multiply
the expression by %283-5i%29%2F%283-5i%29 which equals 1:

%285%2B8i%29%2F%283%2B5i%29%22%22%2A%22%22%283-5i%29%2F%283-5i%29

%28%285%2B8i%29%283-5i%29%29%2F%28%283%2B5i%29%283-5i%29%29

FOIL out the top and bottom:

%2815-25i%2B24i-40i%5E2%29%2F%289-15i%2B15i-25i%5E2%29

%2815-i-40i%5E2%29%2F%289-25i%5E2%29

Now replace i%5E2 by -1:

%2815-i-40%28-1%29%29%2F%289-25%28-1%29%29

%2815-i%2B40%29%2F%289%2B25%29

%2855-i%29%2F34

55%2F34%22%22-%22%22expr%281%2F34%29i

Edwin