SOLUTION: Hello, I am a the daughter of some missionaris to Mexico, and am teaching myself algebra. I am having a hard time understanding about Pure Imaginary Numbers. My text book is tell

Question 170946: Hello, I am a the daughter of some missionaris to Mexico, and am teaching myself algebra. I am having a hard time understanding about Pure Imaginary Numbers. My text book is telling me that i^2=-1, i^3=-i, i^4=1, and so on. I don't understand how they are getting that because they aren't telling me. Could you please help me? I am sure it is pretty simple, but I can't figgure it out!
Found 2 solutions by Mathtut, Earlsdon:
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
This is a cycle: the first two are just definitions of complex numbers so i=i
and ...if you take the sqrt of both these terms you get that is where they come up with

:

:

:

:
then is just and it just keeps up this pattern
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
"Imaginary" Numbers (i), an unfortunate nomenclature, are based on .
=
=
==
==
==
Can you begin to see a pattern here?
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