document.write( "Question 245747: I need to find all the zeros of the function f(x)=x^2+2ix-3.
\n" ); document.write( "I'm trying to use the quadratic equation, but I think I'm doing it wrong.
\n" ); document.write( "Can someone show me step-by-step how to find the zeros of this function? \n" ); document.write( "

Algebra.Com's Answer #179481 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"f%28x%29=x%5E2%2B2ix-3\"$
\n" ); document.write( "You have it right. The quadratic formula is the way to go. With \"a\" = 1, \"b\" = 2i and \"c\" = -3 we get:
\n" ); document.write( " $\"x+=+%28-%282i%29+%2B-+sqrt%28%282i%29%5E2+-+4%281%29%28-3%29%29%29%2F2%281%29\"$
\n" ); document.write( "Now we simplify:
\n" ); document.write( " $\"x+=+%28-%282i%29+%2B-+sqrt%284i%5E2+-+4%281%29%28-3%29%29%29%2F2%281%29\"$
\n" ); document.write( "Since $\"i%5E2+=+-1\"$ :
\n" ); document.write( " $\"x+=+%28-%282i%29+%2B-+sqrt%284%28-1%29+-+4%281%29%28-3%29%29%29%2F2%281%29\"$
\n" ); document.write( " $\"x+=+%28-2i+%2B-+sqrt%28-4+%2B12+%29%29%2F2\"$
\n" ); document.write( " $\"x+=+%28-2i+%2B-+sqrt%288%29%29%2F2\"$
\n" ); document.write( "Since $\"sqrt%288%29+=+sqrt%284%2A2%29+=+sqrt%284%29%2Asqrt%282%29+=+2sqrt%282%29\"$ :
\n" ); document.write( " $\"x+=+%28-2i+%2B-+2sqrt%282%29%29%2F2\"$
\n" ); document.write( "Now we reduce the fraction by canceling common factors. So we factor a 2 out of the numerator:
\n" ); document.write( " $\"x+=+%282%28-i+%2B-+sqrt%282%29%29%29%2F2\"$
\n" ); document.write( "The 2's cancel:
\n" ); document.write( " $\"x+=+-i+%2B-+sqrt%282%29\"$
\n" ); document.write( "or
\n" ); document.write( " $\"x+=+-i+%2B+sqrt%282%29\"$ or $\"x+=+-i+-+sqrt%282%29\"$
\n" ); document.write( "And finally, since we usually write complex numbers with the real part first:
\n" ); document.write( " $\"x+=+sqrt%282%29+%2B+%28-i%29\"$ or $\"x+=+-sqrt%282%29+%2B+%28-i%29\"$ \r
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