document.write( "Question 391971: Write a polynomial equation of least degree with roots: 1, i, and -i.\r
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Algebra.Com's Answer #278174 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
I can say
\n" ); document.write( " $\"x+=+1\"$
\n" ); document.write( " $\"x+=+i\"$
\n" ); document.write( " $\"x+=+-i\"$
\n" ); document.write( "----------
\n" ); document.write( "Now I can say
\n" ); document.write( " $\"x+-+1+=+0\"$
\n" ); document.write( " $\"x+-+i+=+0\"$
\n" ); document.write( " $\"x+-+%28-i%29+=+0\"$
\n" ); document.write( "----------
\n" ); document.write( "Multiplying the left sides:
\n" ); document.write( " $\"%28x+-+1%29%2A%28x+-+i%29%2A%28x+-%28-i%29%29\"$
\n" ); document.write( " $\"%28x+-+1%29%2A%28x%5E2+%2B1%29\"$
\n" ); document.write( " $\"x%5E3++%2B+x+-+x%5E2+-+1\"$
\n" ); document.write( " $\"x%5E3+-+x%5E2+%2B+x+-+1+=+0\"$
\n" ); document.write( "If I substitute $\"x+=+1\"$ , the I get
\n" ); document.write( " $\"1+-+1+%2B+1+-+1+=+0\"$ correct
\n" ); document.write( "and $\"x+=+i\"$ ,
\n" ); document.write( " $\"-i+%2B+1+%2B+i+-+1+=+0\"$ correct
\n" ); document.write( "and $\"x+=+-i\"$
\n" ); document.write( " $\"i+%2B+1+-+i+-+1+=+0\"$ correct
\n" ); document.write( "The tricky part is $\"i%5E2+=+%28-i%29%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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