document.write( "Question 685129: Find the product of (4+5i) and (4-5i) What are pairs of complex numbers like these called? \n" ); document.write( "

Algebra.Com's Answer #424350 by funmath(2933) $\"\"$ $\"About$

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Find the product of (4+5i) and (4-5i) What are pairs of complex numbers like these called?
\n" ); document.write( "These are called \"conjugates\" of each other because they are the same binomials with opposite signs in the middle.
\n" ); document.write( "You need to know that $\"highlight%28i%5E2=-1%29\"$ then you can foil as always...but conjugates always multiply to be the difference of squares...so it is not necessary...but it works every time.
\n" ); document.write( " $\"%284%2B5i%29%284-5i%29\"$
\n" ); document.write( " $\"4%284-5i%29%2B5i%284-5i%29\"$
\n" ); document.write( " $\"16-20i%2B20i-25i%5E2\"$
\n" ); document.write( " $\"16-25i%5E2\"$
\n" ); document.write( "The above is the difference of squares that you can skip to for conjugates.
\n" ); document.write( " $\"16-25%28-1%29\"$
\n" ); document.write( " $\"16%2B25\"$
\n" ); document.write( " $\"highlight%2841%29\"$
\n" ); document.write( "Happy Calculating!!! \n" ); document.write( "

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