document.write( "Question 838942: find the square root of (-15+8i) \n" ); document.write( "

Algebra.Com's Answer #505439 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%28a%2Bbi%29%28a%2Bbi%29=a%5E2%2Babi%2Babi%2B%28bi%29%5E2\"$
\n" ); document.write( " $\"%28a%2Bbi%29%28a%2Bbi%29=%28a%5E2-b%5E2%29%2B2abi\"$
\n" ); document.write( "1. $\"a%5E2-b%5E2=-15\"$
\n" ); document.write( "2. $\"2ab=8\"$
\n" ); document.write( "From eq. 2,
\n" ); document.write( " $\"ab=4\"$
\n" ); document.write( " $\"a=4%2Fb\"$
\n" ); document.write( " $\"a%5E2=16%2Fb%5E2\"$
\n" ); document.write( "Substitute into eq. 1,
\n" ); document.write( " $\"16%2Fb%5E2-b%5E2=-15\"$
\n" ); document.write( " $\"16-b%5E4=-15b%5E2\"$
\n" ); document.write( " $\"b%5E4-15b%5E2-16=0\"$
\n" ); document.write( " $\"%28b%5E2-16%29%28b%5E2%2B1%29=0\"$
\n" ); document.write( "Only the real solution.
\n" ); document.write( " $\"b%5E2-16=0\"$
\n" ); document.write( " $\"b%5E2=16\"$
\n" ); document.write( " $\"b=4\"$
\n" ); document.write( "From eq. 2,
\n" ); document.write( " $\"ab=4\"$
\n" ); document.write( " $\"a%284%29=4\"$
\n" ); document.write( " $\"a=1\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"sqrt%28%28-15%2B8i%29%29=1%2B4i\"$ \n" ); document.write( "

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