SOLUTION: 1) If a-bi = 2+i / 1-i which of the following is true A) a=1 b=3 B) a=-1/2 b=-3/2 C) a=3/2 b=1/2 D)a=1/2 b=-3/2

Algebra ->  Finance -> SOLUTION: 1) If a-bi = 2+i / 1-i which of the following is true A) a=1 b=3 B) a=-1/2 b=-3/2 C) a=3/2 b=1/2 D)a=1/2 b=-3/2       Log On


   

Question 1088902: 1) If a-bi = 2+i / 1-i which of the following is true
A) a=1 b=3
B) a=-1/2 b=-3/2
C) a=3/2 b=1/2
D)a=1/2 b=-3/2
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

%28+a-bi+%29=+%282%2Bi%29+%2F+%281-i%29
%28+a-bi+%29=+%28%282%2Bi%29+%281%2Bi%29%29+%2F%28+%281-i%29+%281%2Bi%29%29
%28+a-bi+%29=+%282%2B2i%2Bi%2Bi%5E2%29+%2F+%281%5E2-i%5E2%29

%28+a-bi+%29=+%282%2B3i%2B%28-1%29%29+%2F+%281-%28-1%29%29+
%28+a-bi+%29=+%282%2B3i-1%29+%2F+%281%2B1%29

%28+a-bi+%29=+%281%2B3i%29+%2F+2
2%28+a-bi+%29=+%281%2B3i%29


2a=1=> highlight%28a=1%2F2%29
-2bi=3i...cancel i
-2b=3
highlight%28green%28b=-3%2F2%29%29

and, your answer is:
D)highlight%28a=1%2F2%29, highlight%28green%28b=-3%2F2%29%29