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

Question 1058696: (1+i)/(1-2i)
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!

Multiplication by 1 does not change the rational expression given.
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
(1+i)/(1-2i)
~~~~~~~~~~~~~~~~~

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

= ( 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 ) = Then the numerator is equal to 1 + 2i + i + i*(2i) = = 1 + 3i - 2 = -1 + 3i (since = -1) The denominator is eqial to = = 1 - 4*(-1) = 1 + 4 = 5 ( again, since = -1 ) Hence, the entire fraction is = = -0.2 + 0.6i. Answer. = -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".

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