SOLUTION: Hi there! I just started highschool at a collegiate school. I am so thankful I got in, and I would like to learn as much as possible. But due to hurricane Irma, school was cancelle

Question 1093964: Hi there! I just started highschool at a collegiate school. I am so thankful I got in, and I would like to learn as much as possible. But due to hurricane Irma, school was cancelled and therefore my teacher did not have time to teach us. I know this is pretty simple, and I found the answers online, but I want to learn how to do it and get the answer myself. Here are a few problems I cannot get. Below is my work that I know is wrong.
i^7
(i^3)^2 x i
-i x -i = i
i x i = i
i^49
i^99
i^91
i^473
i^2001
i^8 + i^9 + i^10
Please help me asap. I have more questions like this, but I want to do most of it myself.

Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
i^7
(i^3)^2 x i
-i x -i = i
i x i = i
i^49
i^99
i^91
i^473
i^2001
i^8 + i^9 + i^10
-----------------------
i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1
-----
It's "modulus 4" of a sort
==============
i^7 = i^4*i^3 = i^3
= i^2*i = -i
================
(i^3)^2 x i
-i x -i = i
i x i = i
---
i^49
= i^48*i = i
===============
i^99
= i^96*i^3 = -i
===============
i^91
i^473
i^2001
i^8 + i^9 + i^10
= 1 + i - 1
= i

Answer by ikleyn(52780)   (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.

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