SOLUTION: which are the real part and imaginary part of the complex number [(1+i)/(1-i)]-[(1-i)-(1+i)]

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Question 1100597: which are the real part and imaginary part of the complex number [(1+i)/(1-i)]-[(1-i)-(1+i)]
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
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which are the real part and imaginary part of the complex number [(1+i)/(1-i)]-[(1-i)-(1+i)]
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%281%2Bi%29%2F%281-i%29 = %28%281%2Bi%29%2A%281%2Bi%29%29%2F%28%281-i%29%2A%281%2Bi%29%29 = %281%2B2i-i%5E2%29%2F%281-i%5E2%29 = %282%2B2i%29%2F2 = 1 + i.


[(1-i) - (1+i)] = -2i.


Therefore 


%281%2Bi%29%2F%281-i%29+-+%28%281-i%29-%281%2Bi%29%29 = 1 + i - 2i = 1 - i.


The real part of this complex number is 1.  The imaginary part is -i.


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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

    - Solved problems on taking roots of complex numbers
    - Solved problems on arithmetic operations on complex numbers
    - Solved problem on taking square root of complex number
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".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.