SOLUTION: Express the following in the form of a+ib, a, b belongs to R, i=square root of -1. State the values of a and b (2+i)upon (3-i)(1+2i)

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Express the following in the form of a+ib, a, b belongs to R, i=square root of -1. State the values of a and b (2+i)upon (3-i)(1+2i)      Log On


   

Question 888267: Express the following in the form of a+ib, a, b belongs to R, i=square root of -1. State the values of a and b
(2+i)upon (3-i)(1+2i)
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Do you mean, or you must mean, this:
%282%2Bi%29%2F%28%283-i%29%281%2B2i%29%29

Simplify for denominator first.
%282%2Bi%29%2F%283-i%2B6i-2i%5E2%29

%282%2Bi%29%2F%283%2B5i%2B2%29

%282%2Bi%29%2F%285%2B5i%29


Use the conjugate of the denominator.
%28%282%2Bi%29%2F%285%2B5i%29%29%28%285-5i%29%2F%285-5i%29%29, which is multiplication by 1,

%28%282%2Bi%29%285-5i%29%29%2F%285%5E2-5%5E2%2Ai%5E2%29, notice, difference of two squares...

%2810%2B5i-10i-5i%5E2%29%2F%2825%2B25%29

%2810%2B5%2B%28-5i%29%29%2F50

%2815-5i%29%2F50

5%283-i%29%2F%285%2A10%29

highlight%28%283%2F10%29-%281%2F10%29i%29