SOLUTION: (1+i)/(1-2i)

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Question 1058696: (1+i)/(1-2i)
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
1=%28%281%2B2i%29%2F%281%2B2i%29%29

Multiplication by 1 does not change the rational expression given.

Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.
(1+i)/(1-2i)
~~~~~~~~~~~~~~~~~

More educated people add the courtesy words "Simplify please" . . . 

  %281%2Bi%29%2F%281-2i%29 =        ( multiply the numerator and the denominator by the number (1+2i), which is conjugate to the number in the denominator.
                    The value of the fraction doesn't change and remains the same after this operation )


= %28%281%2Bi%29%2A%281%2B2i%29%29%2F%28%281-2i%29%2A%281%2B2i%29%29


Then the numerator is equal to  1 + 2i + i + i*(2i) = 1+%2B+3i+%2B+2%2Ai%5E2 = 1 + 3i - 2 = -1 + 3i   (since i%5E2 = -1)

The denominator is eqial to  1%5E2+-+%282i%29%5E2 = 1+-+4%2Ai%5E2 = 1 - 4*(-1) = 1 + 4 = 5   ( again, since i%5E2 = -1 )

Hence, the entire fraction is

%281%2Bi%29%2F%281-2i%29 = %28-1+%2B+3i%29%2F5 = -0.2 + 0.6i.


Answer.  %281%2Bi%29%2F%281-2i%29 = -0.2 + 0.6i.

There are lessons on complex numbers in this site
    - Complex numbers and arithmetic 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 under the topic "Complex numbers".