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

Algebra ->  Algebra  -> Complex Numbers Imaginary Numbers Solvers and Lesson -> 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      Log On

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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) About Me  (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 i%5E2=-1%29...if you take the sqrt of both these terms you get i=sqrt%28-1%29 that is where they come up with i%5E2=-1



i=i
:
i%5E2=-1
:
i%5E3=i%5E2%28i%29=%28-1%29i=-i
:
i%5E4=i%5E2i%5E2=%28-1%29%28-1%29=1
:
then i%5E5 is just i%5E4%28i%29=i and it just keeps up this pattern

Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
"Imaginary" Numbers (i), an unfortunate nomenclature, are based on sqrt%28-1%29.
i+=+sqrt%28-1%29=i
i%5E2+=+%28sqrt%28-1%29%29%5E2=-1
i%5E3+=+%28sqrt%28-1%29%29%5E3=%28sqrt%28-1%29%29%5E2%2A%28sqrt%28-1%29%29+=+-1%2Ai=-i
i%5E4+=+%28sqrt%28-1%29%29%5E4=%28sqrt%28-1%29%29%5E2%2A%28sqrt%28-1%29%29%5E2+=+%28-1%29%28-1%29=1
i%5E5+=+%28sqrt%28-1%29%29%5E5=%28sqrt%28-1%29%29%5E2%2A%28sqrt%28-1%29%29%5E3+=+-1%2A%28-i%29= i
Can you begin to see a pattern here?