document.write( "Question 100060: given the following two complex numbers, a=3+7i and b=-2-2i,calculate the following
\n" ); document.write( "a+b
\n" ); document.write( "a-b
\n" ); document.write( "a*b
\n" ); document.write( "a/b \n" ); document.write( "

Algebra.Com's Answer #72864 by timmy1729(23) $\"\"$ $\"About$

You can put this solution on YOUR website!
given the following two complex numbers, a=3+7i and b=-2-2i,calculate the following
\n" ); document.write( "a+b
\n" ); document.write( "a-b
\n" ); document.write( "a*b
\n" ); document.write( "a/b
\n" ); document.write( "Ok, for the most part, treat i like a variable. $\"a+%2B+b+=+3+%2B+7i+-2+-+2i\"$
\n" ); document.write( " $\"3+%2B+7i+-2+-+2i+=+1%2B5i\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"a+-+b+=+3+%2B+7i+-%28-2+-+2i%29+=+3+%2B+7i+%2B+2+%2B+2i+=+5+%2B+9i\"$ \r
\n" ); document.write( "\n" ); document.write( "a*b is just simply: $\"%283%2B7i%29%28-2-2i%29+=+-6+-+6i+-+14i+-+14i%5E2\"$
\n" ); document.write( "Remember that i^2 = -1. So we simplify into: $\"-6+-+20i+%2B+14+=+8+-+20i\"$ \r
\n" ); document.write( "\n" ); document.write( "a/b is $\"%283%2B7i%29%2F%28-2-2i%29\"$
\n" ); document.write( "To simplify, you multiply the numerator and denominator by the denominator's complex conjugate which is -2+2i.
\n" ); document.write( " $\"%28%283%2B7i%29%28-2%2B2i%29%29%2F%28%28-2-2i%29%28-2%2B2i%29%29\"$
\n" ); document.write( " $\"%28-6%2B6i-14i-14%29%2F%284+-4i+%2B+4i+%2B4%29\"$
\n" ); document.write( " $\"%28-20-8i%29%2F%288%29\"$
\n" ); document.write( " $\"%284%28-5-2i%29%29%2F%288%29\"$
\n" ); document.write( " $\"%28-5-2i%29%2F2\"$ \n" ); document.write( "

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