SOLUTION: divide the complex numbers and write the final answer in the form a+bi -10+i ______ 2+i I appreciate any help =D Thank you =D

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: divide the complex numbers and write the final answer in the form a+bi -10+i ______ 2+i I appreciate any help =D Thank you =D      Log On


   

Question 294966: divide the complex numbers and write the final answer in the form a+bi
-10+i
______
2+i
I appreciate any help =D
Thank you =D
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28-10%2Bi%29%2F%282%2Bi%29 Start with the given expression.


%28%28-10%2Bi%29%2F%282%2Bi%29%29%28%282-i%29%2F%282-i%29%29 Multiply the fraction by %282-i%29%2F%282-i%29.


%28%28-10%2Bi%29%282-i%29%29%2F%28%282%2Bi%29%282-i%29%29 Combine the fractions.


FOIL the numerator.


FOIL the denominator.


%28-20%2B10i%2B2i-i%5E2%29%2F%284-2i%2B2i-i%5E2%29 Multiply.


%28-20%2B10i%2B2i-%28-1%29%29%2F%284-2i%2B2i-%28-1%29%29 Replace i%5E2 with -1.


%28-19%2B12i%29%2F%285%29 Combine like terms.


%28-19%29%2F%285%29%2B%28%2812%29%2F%285%29%29i Break up the fraction.


-19%2F5%2B%2812%2F5%29i Reduce.


So %28-10%2Bi%29%2F%282%2Bi%29=-19%2F5%2B%2812%2F5%29i which is in standard form a%2Bbi where a=-19%2F5 and b=12%2F5