document.write( "Question 581638: How do you solve the problem (1-4i)/(2+3i) \r
\n" ); document.write( "\n" ); document.write( "i is an imaginary number (the square root of -1)\r
\n" ); document.write( "\n" ); document.write( "Also, how would you find the equation of a circle with a diameter AB, given that the coordinates of a and B are (-6,1) and (4,-5). What is the answer in standard form \n" ); document.write( "

Algebra.Com's Answer #371753 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "The denominator is 2+3i.  Its conjugate is 2-3i \r\n" );
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document.write( "(change the sign of the term containing i)\r\n" );
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document.write( "Multiply by the unit fraction formed by putting the con=jugate\r\n" );
document.write( "of the denominator over itself: \r\n" );
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document.write( "Multiply (FOIL) out the top and bottom:\r\n" );
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document.write( "Combine the like terms. (the two middle terms in the bottom cancel)  \r\n" );
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document.write( "Substitute (-1) for i²\r\n" );
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document.write( "Simplify\r\n" );
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document.write( "Combine like terms:\r\n" );
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document.write( "Divide the -10 and the -11 each by 13\r\n" );
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document.write( "Also, how would you find the equation of a circle with a diameter AB, given that the coordinates of a and B are (-6,1) and (4,-5). What is the answer in standard form:\r\n" );
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document.write( "We need the the radius r and the center (h,k) and then we can \r\n" );
document.write( "substitute thes is the equation for a circle:\r\n" );
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document.write( "(x - h)² + (y - k)² = r²\r\n" );
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document.write( "Let's graph the points and draw the diameter:\r\n" );
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document.write( "We will use the distance formula to find the diameter, which we will take\r\n" );
document.write( "on half of for the radius. The distance formula is:\r\n" );
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document.write( "d = \r\n" );
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document.write( "d =  =  =  =  = \r\n" );
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document.write( "d =  =  = \r\n" );
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document.write( "So the diameter is  and the radius is one-half of that \r\n" );
document.write( "diameter which is \r\n" );
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document.write( "The midpoint of any diameter is the center.  So we use the midpoint formula:\r\n" );
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document.write( "Midpoint =  = \r\n" );
document.write( " =  =  = \r\n" );
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document.write( "So the center is (h,k) = C(-1,-2) and the radius is r = .\r\n" );
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document.write( "Substituting in\r\n" );
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document.write( "(x - h)² + (y - k)² = r²\r\n" );
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document.write( "(x - (-1))² + (y - (-2))² = ()²\r\n" );
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document.write( "(x + 1)² + (y + 2)² = 34\r\n" );
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document.write( "Edwin

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