document.write( "Question 397869: (-2+sqrt(-100) \n" ); document.write( "

Algebra.Com's Answer #282083 by jsmallt9(3759) $\"\"$ $\"About$

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$\"-2%2Bsqrt%28-100%29\"$
\n" ); document.write( "With a negative number inside the square root, this expression represents a complex number. The first thing to do with this is write the square root in terms of \"i\", which is $\"sqrt%28-1%29\"$ . So we factor out -1:
\n" ); document.write( " $\"-2%2Bsqrt%28-1%2A100%29\"$
\n" ); document.write( "Then we use a property of radicals, $\"root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29%2Aroot%28a%2C+q%29\"$ , to write the square root of the product as the product of the square roots of the factors:
\n" ); document.write( " $\"-2%2Bsqrt%28-1%29%2Asqrt%28100%29\"$
\n" ); document.write( "Not only does the $\"sqrt%28-1%29\"$ simplify to \"i\", but $\"sqrt%28100%29\"$ also simplifies to 10:
\n" ); document.write( "-2 + i*10
\n" ); document.write( "or
\n" ); document.write( "-2 + 10i \n" ); document.write( "

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