SOLUTION: solve z^4 -i=0

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Question 1181954: solve z^4 -i=0
Answer by ikleyn(52887) About Me  (Show Source):
You can put this solution on YOUR website!
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It is about finding the roots of the pure imaginary number  " i "  of the fourth degree.


Since  i = cis%28pi%2F2%29,  the roots of the fourth degree of  " i "  are



1)  cis%28pi%2F8%29;


2)  cis%28pi%2F8+%2B+pi%2F2%29 = cis%28pi%2F8+%2B+4pi%2F8%29 = cis%285pi%2F8%29;


3)  cis%28pi%2F8+%2B+2pi%2F2%29 = cis%28pi%2F8+%2B+8pi%2F8%29 = cis%289pi%2F8%29;


4)  cis%28pi%2F8+%2B+3pi%2F2%29 = cis%28pi%2F8+%2B+12pi%2F8%29 = cis%2813pi%2F8%29.

Solved.     //     All solutions to the given equation are listed.

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On complex numbers,  see introductory lessons
    - 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

    - 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
    - Solving polynomial equations in complex domain
    - Miscellaneous problems on complex numbers
in this site.

Also,  you have this free of charge online textbook on  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.