Question 1058696
.
(1+i)/(1-2i)
~~~~~~~~~~~~~~~~~


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


<pre>
  {{{(1+i)/(1-2i)}}} =        ( 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 )


= {{{((1+i)*(1+2i))/((1-2i)*(1+2i))}}}


Then the numerator is equal to  1 + 2i + i + i*(2i) = {{{1 + 3i + 2*i^2}}} = 1 + 3i - 2 = -1 + 3i   (since {{{i^2}}} = -1)

The denominator is eqial to  {{{1^2 - (2i)^2}}} = {{{1 - 4*i^2}}} = 1 - 4*(-1) = 1 + 4 = 5   ( again, since {{{i^2}}} = -1 )

Hence, the entire fraction is

{{{(1+i)/(1-2i)}}} = {{{(-1 + 3i)/5}}} = -0.2 + 0.6i.


<U>Answer</U>.  {{{(1+i)/(1-2i)}}} = -0.2 + 0.6i.
</pre>

There are lessons on complex numbers in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/Complex-numbers-and-arithmetical-operations.lesson>Complex numbers and arithmetic operations on them</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/Complex-plane.lesson>Complex plane</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/Addition-and-subtraction-of-complex-numbers-in-complex-plane.lesson>Addition and subtraction of complex numbers in complex plane</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/Multiplication-and-division-of-complex-numbers-in-complex-plane-.lesson>Multiplication and division of complex numbers in complex plane</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/Raising-a-complex-number-to-an-integer-power.lesson>Raising a complex number to an integer power</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/complex/How-to-take-a-root-of-a-complex-number.lesson>How to take a root of a complex number</A>


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/Solved-problems-on-taking-roots-of-complex-numbers.lesson>Solved problems on taking roots of complex numbers</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/Solved-problems-on-arithmetic-operations-on-complex-numbers.lesson>Solved problems on arithmetic operations on complex numbers</A>

in this site.



Also, you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


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