document.write( "Question 180687: I need help please show me an example of a complex roots equation. Thanks \n" ); document.write( "

Algebra.Com's Answer #135421 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Suppose the roots are $\"i+%2B+1\"$ and $\"i+-+1\"$ , then
\n" ); document.write( "the equation can be factored into
\n" ); document.write( " $\"%28x+-+%281+%2B+i%29%29\"$ and $\"%28x+-+%281+-+i%29%29\"$ , so
\n" ); document.write( " $\"%28x+-+%281+%2B+i%29%29%28x+-+%281+-+i%29%29+=+0\"$
\n" ); document.write( "Note that if you replace $\"x\"$ by either $\"1+%2B+i\"$ or $\"1+-+i\"$ ,
\n" ); document.write( "Then the equation is solved
\n" ); document.write( "Now multiplying the factors:
\n" ); document.write( " $\"x%5E2+-%281+%2B+i%29x+-+%281+-+i%29x+%2B+%281+%2B+i%29%281+-+i%29+=+0\"$
\n" ); document.write( " $\"x%5E2+-+x+-+ix+-+x+%2B+ix+%2B+1+%2B+i+-+i+-+i%5E2+=+0\"$
\n" ); document.write( "(note that $\"i%5E2+=+-1\"$ and $\"-i%5E2+=+%2B1\"$ )
\n" ); document.write( " $\"x%5E2+-+x+-+ix+-+x+%2B+ix+%2B+1+%2B+i+-+i+-+i%5E2+=+x%5E2+-+2x+%2B+2\"$
\n" ); document.write( " $\"x%5E2+-+2x+%2B+2+=+0\"$ is the equation to find roots
\n" ); document.write( " $\"y+=+x%5E2+-+2x+%2B+2\"$ is the complete complex roots equation
\n" ); document.write( "There are 2 complex roots to this equation,
\n" ); document.write( " $\"1+%2B+i\"$ and $\"1+-+i\"$
\n" ); document.write( "Graphing it, you can see it doesn't intersect the x-axis, where
\n" ); document.write( "real roots would be:
\n" ); document.write( " $\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2+-+2x+%2B+2%29+\"$ \r
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