SOLUTION: simplify. Write your answers in the form of a+bi where a and b are red numbers. (1-i)/(-9+2i) the answer is -11/85+7/85i

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: simplify. Write your answers in the form of a+bi where a and b are red numbers. (1-i)/(-9+2i) the answer is -11/85+7/85i      Log On


   

Question 922474: simplify. Write your answers in the form of a+bi where a and b are red numbers.
(1-i)/(-9+2i)
the answer is -11/85+7/85i
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1-i/-9+2i
-----------
Multiply the NUM and DEN by the conjugate of the DEN -9-2i
= (1-i)*(-9-2i)/(-9+2i)*(-9-2i)
= (-9 + 7i - 2)/(81+4)
= (-11 + 7i)/85

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
%281-i%29%2F%28-9%2B2i%29

The conjugate of the denominator -9+2i is formed by changing 
the sign of only the imaginary part, getting -9-2i.

So we multiply by %28-9-2i%29%2F%28-9-2i%29 which just equals 1.

%281-i%29%2F%28-9%2B2i%29%22%D7%22%28-9-2i%29%2F%28-9-2i%29

%28%281-i%29%28-9-2i%29%29%2F%28%28-9%2B2i%29%28-9-2i%29%29 

Use FOIL on numerator and denominator:

%28-9-2i%2B9i%2B2i%5E2%29%2F%2881%2B18i-18i-4i%5E2%29

%28-9%2B7i%2B2i%5E2%29%2F%2881-4i%5E2%29

Replace iČ by -1

%28-9%2B7i%2B2%28-1%29%29%2F%2881-4%28-1%29%29

%28-9%2B7i-2%29%2F%2881%2B4%29

%28-11%2B7i%29%2F85

-11%2F85%2B%287i%29%2F85

-11%2F85%2Bexpr%287%2F85%29i

Edwin