SOLUTION: find Re(z1z2/z1) and Im(1/z1z2) if z1=2-i,z2=-2+i

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Question 1055627: find Re(z1z2/z1) and Im(1/z1z2) if z1=2-i,z2=-2+i
Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
.
find Re(z1z2/z1) and Im(1/z1z2) if z1=2-i,z2=-2+i
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1.  %28z1%2Az2%29%2Fz1 = z2 = -2 + i.

    Therefore, Re%28%28z1%2Az2%29%2Fz1%29 = Re(z2) = -2.


2.  1%2F%28z1%2Az2%29 = 1%2F%28%282-i%29%2A%28-2%2Bi%29%29 = 1%2F%28-4+%2B1+%2B+2i%29 = 1%2F%28-3%2B2i%29 = %28-3-2i%29%2F%28%28-3%2B2i%29%2A%28-3-2i%29%29 = %28-3-2i%29%2F%289%2B4%29 = %28-3-2i%29%2F13 = -3%2F13+-i%2A%282%2F13%29.

    Therefore,  Im%281%2F%28z1%2Az2%29%29 = -2%2F13.

There is a bunch of my 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
    - How to take a square 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.