document.write( "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! \n" ); document.write( "

Algebra.Com's Answer #126207 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
\"Imaginary\" Numbers (i), an unfortunate nomenclature, are based on $\"sqrt%28-1%29\"$ .
\n" ); document.write( " $\"i+=+sqrt%28-1%29\"$ = $\"i\"$
\n" ); document.write( " $\"i%5E2+=+%28sqrt%28-1%29%29%5E2\"$ = $\"-1\"$
\n" ); document.write( " $\"i%5E3+=+%28sqrt%28-1%29%29%5E3\"$ = $\"%28sqrt%28-1%29%29%5E2%2A%28sqrt%28-1%29%29+=+-1%2Ai\"$ = $\"-i\"$
\n" ); document.write( " $\"i%5E4+=+%28sqrt%28-1%29%29%5E4\"$ = $\"%28sqrt%28-1%29%29%5E2%2A%28sqrt%28-1%29%29%5E2+=+%28-1%29%28-1%29\"$ = $\"1\"$
\n" ); document.write( " $\"i%5E5+=+%28sqrt%28-1%29%29%5E5\"$ = $\"%28sqrt%28-1%29%29%5E2%2A%28sqrt%28-1%29%29%5E3+=+-1%2A%28-i%29\"$ = $\"i\"$
\n" ); document.write( "Can you begin to see a pattern here? \n" ); document.write( "

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