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 #126206 by Mathtut(3670) $\"\"$ $\"About$

You can put this solution on YOUR website!
This is a cycle: the first two are just definitions of complex numbers so i=i
\n" ); document.write( "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 $\"i%5E2=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"i=i\"$
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\n" ); document.write( " $\"i%5E2=-1\"$
\n" ); document.write( ":
\n" ); document.write( " $\"i%5E3=i%5E2%28i%29=%28-1%29i=-i\"$
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\n" ); document.write( " $\"i%5E4=i%5E2i%5E2=%28-1%29%28-1%29=1\"$
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\n" ); document.write( "then $\"i%5E5\"$ is just $\"i%5E4%28i%29=i\"$ and it just keeps up this pattern \n" ); document.write( "

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