.
(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".