SOLUTION: Evaluate this quotient of complex numbers. State answer in a+bi format 3-2i/1+i How?

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Question 1057505: Evaluate this quotient of complex numbers. State answer in a+bi format
3-2i/1+i
How?
Found 3 solutions by josgarithmetic, MathTherapy, ikleyn:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
"Evaluate" means, to find its value. You already have the number; it just is not simplified. Best understanding may be to simplify your number.

%28%283-2i%29%2F%281%2Bi%29%29

%28%283-2i%29%2F%281%2Bi%29%29%28%281-i%29%2F%281-i%29%29--------multipliciation by 1, using "conjugate" of the denominator

UNDERSTAND THAT i%5E2=-1.
%28%283-2i%29%281%2Bi%29%29%2F%281-i%5E2%29

%283-2i%2B3i-2i%5E2%29%2F2

%283%2Bi%2B2%29%2F2

%285%2Bi%29%2F2

5%2F2%2B%281%2F2%29i

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
Evaluate this quotient of complex numbers. State answer in a+bi format
3-2i/1+i
How?
%283+-+2i%29%2F%281+%2B+i%29

%283+-+2i%29%281+-+i%29%2F%281+%2B+i%29%281+-+i%29 ------- Multiplying NUMERATOR and DENOMINATOR by CONJUGATE of DENOMINATOR

%283+-+3i+-+2i+%2B+2i%5E2%29%2F%281+-+i%5E2%29 ----- FOILing/DISTRIBUTING 

%283+-+5i+%2B+2i%5E2%29%2F%281+-+i%5E2%29

%283+-+5i+%2B+2%28-+1%29%29%2F%281+-+-+1%29 ------- Replacing i%5E2 with  - 1

%283+-+5i+-+2%29%2F%281+%2B+1%29

%281+-+5i%29%2F2

highlight_green%281%2F2+-+%285%2F2%29i%29 ------- a + bi format

A PIECE OF ADVICE:  Ignore all other answers that are DISSIMILAR to the one above!

Answer by ikleyn(52831) About Me  (Show Source):
You can put this solution on YOUR website!
.
There is a bunch of lessons on complex numbers
    - 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
    - Raising a complex number to an integer power
    - How to take a root of a complex number

    - Solved problems on taking roots of complex numbers
    - Solved problems on arithmetic operations on complex numbers
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.