SOLUTION: Simplify each imaginary number using the properties of exponents. • i^71 • i^121

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Question 1092799: Simplify each imaginary number using the properties of exponents.
• i^71
• i^121
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
i^1=i
i^2=-1
i^3=-i
i^4=1
and they repeat.
So i^71 is 71/4 is 17 with remainder 3, so it is i^3=-i
i^121 is 121/4 or 30 with remainder 1, so it is i.

Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
.
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
    - Raising a complex number to an integer power

    - 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".


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.