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 1088883: 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

Found 3 solutions by josgarithmetic, math_helper, ikleyn:
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
%282%2Bi%29%2F%281-i%29

%28%282%2Bi%29%2F%281-i%29%29%28%281%2Bi%29%2F%281%2Bi%29%29
Continue with this and simplify it,... to get
1%2B3i%2F2.


If no mistakes made (steps done off the page), then for a-bi
system%28a=1%2Cand%2Cb=-3%2F2%29.

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
+%28+2%2Bi+%29%2F%281+-+i%29+%2A+%281%2Bi%29+%2F+%281%2Bi%29+
= ++%282%2B2i%2Bi%2Bi%5E2%29+%2F+%281%2Bi-i-i%5E2+%29+
= ++%281+%2B+3i%29%2F2+
= ++%281%2F2%29+%2B+%283%2F2%29i+
—
Comparing this to a - bi, we notice +highlight%28a+=+1%2F2%29+ and +highlight%28b+=+-3%2F2%29+

Answer by ikleyn(52769) About Me  (Show Source):
You can put this solution on YOUR website!
.

The correct answer is +highlight%28a+=+1%2F2%29+ and +highlight%28b+=+-3%2F2%29+.

The answer by @josgarithmetic is INCORRECT.


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On complex numbers, see introductory lessons
    - Complex numbers and arithmetical operations on them
    - Complex plane
    - Addition and subtraction of complex numbers in complex plane
    - Multiplication and division of complex numbers in complex plane
in this site.


Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Complex numbers".