document.write( "Question 133075: Hello!
\n" ); document.write( "I need help with a few problems that I'm having difficulty with.
\n" ); document.write( "1) [(1+i)/i] - [(3)/(4-i)]
\n" ); document.write( "For the common denominator, I got i(4-i)= 4i-1
\n" ); document.write( "Do you multiply this normally or do you need a conjugate?\r
\n" ); document.write( "\n" ); document.write( "2) (sqrt-15) * (sqrt-15)
\n" ); document.write( "I really do not understand this problem.\r
\n" ); document.write( "\n" ); document.write( "Any help would be greatly appreciated! Thank you!
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #97312 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
I need help with a few problems that I'm having difficulty with.
\n" ); document.write( "1) \"%281%2Bi%29%2Fi+-+3%2F%284-i%29\"
\n" ); document.write( "For the common denominator, I got \"i%284-i%29\" = \"4i-1\"
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document.write( "That's wrong. \"i%284-i%29\" = \"4i-i%5E2\" = \r\n" );
document.write( "Replace \"i%5E2\" by \"-1\"\r\n" );
document.write( "\"4i-%28-1%29\" = \"4i%2B1\" = \"1%2B4i\"\r\n" );
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document.write( "But you shouldn't have tried to multiply it out yet anyway.\r\n" );
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document.write( "

\n" ); document.write( "Do you multiply this normally or do you need a conjugate?
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document.write( "Here's the whole thing, starting from scratch:\r\n" );
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document.write( "\"%281%2Bi%29%2Fi+-+3%2F%284-i%29\"\r\n" );
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document.write( "The LCD = i(4-i)\r\n" );
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document.write( "DO NOT MULTIPLY THAT OUT YET!  \r\n" );
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document.write( "The denominator of the first fraction needs the factor \"%284-i%29\"\r\n" );
document.write( "in order to become the LCD, so we multiply it by \"%284-i%29%2F%284-i%29\"\r\n" );
document.write( "which is just 1, so it won't affect the value to multiply the first\r\n" );
document.write( "fraction by that:\r\n" );
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document.write( "\"+%28+%281%2Bi%29%2Fi+%29%28+%284-i%29%2F%284-i%29+%29+-+3%2F%284-i%29++\"\r\n" );
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document.write( "The denominator of the second fraction needs the factor \"i\"\r\n" );
document.write( "in order to become the LCD, so we multiply it by \"i%2Fi\"\r\n" );
document.write( "which is just 1, so it won't affect the value to multiply the second\r\n" );
document.write( "fraction by that:\r\n" );
document.write( "\r\n" );
document.write( "\"+%28+%281%2Bi%29%2Fi+%29%28+%284-i%29%2F%284-i%29+%29+-+%283%2F%284-i%29%29%28i%2Fi%29\"\r\n" );
document.write( "\r\n" );
document.write( "Indicate the multiplication of the numerators and the denominators:\r\n" );
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document.write( "\"+%28%281%2Bi%29%284-i%29%29%2F%28i%284-i%29%29+-+%283i%29%2F%28%284-i%29i%29\"\r\n" );
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document.write( "Now use FOIL on the left top:\r\n" );
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document.write( "\"%281%2Bi%29%284-i%29\" = \"4-i%2B4i-i%5E2\" = \"4%2B3i-i%5E2\" = \r\n" );
document.write( "Now replace \"i%5E2\" by \"-1\"\r\n" );
document.write( "\"4%2B3i-%28-1%29\" = \"4%2B3i%2B1\" = \"5%2B3i\" and replace the left top by that:\r\n" );
document.write( "\r\n" );
document.write( "\"+%285%2B3i%29%2F%28i%284-i%29%29+-+%283i%29%2F%28%284-i%29i%29\"\r\n" );
document.write( " \r\n" );
document.write( "Distribute the left bottom\r\n" );
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document.write( "\"i%284-i%29\" = \"4i-i%5E2\" = \r\n" );
document.write( "Replace \"i%5E2\" by \"-1\"\r\n" );
document.write( "\"4i-%28-1%29\" = \"4i%2B1\" = \"1%2B4i\" and\r\n" );
document.write( "replace the left bottom by that:\r\n" );
document.write( "\r\n" );
document.write( "\"+%285%2B3i%29%2F%281%2B4i%29+-+%283i%29%2F%28%284-i%29i%29\"\r\n" );
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document.write( "The right bottom is the same as the left bottom:\r\n" );
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document.write( "\"%284-i%29i\" = \"i%284-i%29\" = \"4i-i%5E2\" =\r\n" );
document.write( "Replace \"i%5E2\" by \"-1\"\r\n" );
document.write( "\"4i-%28-1%29\" = \"4i%2B1\" = \"1%2B4i\" \r\n" );
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document.write( "So replace the right bottom by that:\r\n" );
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document.write( "\"+%285%2B3i%29%2F%281%2B4i%29+-+%283i%29%2F%281%2B4i%29\"\r\n" );
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document.write( "Now combine the numerators over the common denominator:\r\n" );
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document.write( "\"+%285%2B3i-3i%29%2F%281%2B4i%29\"\r\n" );
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document.write( "Collect like terms on top:\r\n" );
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document.write( "\"+5%2F%281%2B4i%29\"\r\n" );
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document.write( "Now we are ready to use the conjugate of the bottom.\r\n" );
document.write( "We multiply by \"%281-4i%29%2F%281-4i%29\" which again just\r\n" );
document.write( "equals to 1 so it will not affect the value:\r\n" );
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document.write( "\"+%285%2F%281%2B4i%29%29%28%281-4i%29%2F%281-4i%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Indicate the multiplication of the numerators and\r\n" );
document.write( "denominators:\r\n" );
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document.write( "\"+%285%281-4i%29%29%2F%28%281%2B4i%29%281-4i%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Distribute the top and use FOIL on the bottom:\r\n" );
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document.write( "\"+%285-20i%29%2F%281-4i%2B4i-16i%5E2%29%29\"\r\n" );
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document.write( "Combine like terms:\r\n" );
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document.write( "\"+%285-20i%29%2F%281-16i%5E2%29%29\"\r\n" );
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document.write( "Replace \"i%5E2\" by \"-1\"\r\n" );
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document.write( "\"+%285-20i%29%2F%281-16%28-1%29%29%29\"\r\n" );
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document.write( "\"+%285-20i%29%2F%281%2B16%29\"\r\n" );
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document.write( "Combine like terms:\r\n" );
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document.write( "\"+%285-20i%29%2F%2817%29\"\r\n" );
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document.write( "Make two fractions:\r\n" );
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document.write( "\"5%2F17-%2820i%29%2F17\"\r\n" );
document.write( "\r\n" );
document.write( "and write the answer in form \"A%2BBi\"\r\n" );
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document.write( "\"5%2F17-20%2F17\"\"i\"\r\n" );
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\r
\n" ); document.write( "\n" ); document.write( "2) \"%28sqrt%28-15%29%29+%2A+%28sqrt%28-15%29%29\"
\n" ); document.write( "I really do not understand this problem.
\n" ); document.write( "Any help would be greatly appreciated! Thank you!
\n" ); document.write( "
\r\n" );
document.write( "Write \"-15\" as \"%2815%29%28-1%29\"\r\n" );
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document.write( "\"+sqrt%28%2815%29%28-1%29%29+%2A+sqrt%28%2815%29%28-1%29%29\" \r\n" );
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document.write( "Take individual square roots of factors under radicals\r\n" );
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document.write( "\"+sqrt%2815%29sqrt%28-1%29+%2A+sqrt%2815%29sqrt%28-1%29\"\r\n" );
document.write( "\r\n" );
document.write( "Replace \"sqrt%28-1%29\" by \"i\"\r\n" );
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document.write( "\"+sqrt%2815%29%2Ai+%2A+sqrt%2815%29%2Ai\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28sqrt%2815%29%29%5E2i%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "Replace \"%28sqrt%2815%29%29%5E2\" by 15 and \"i%5E2\" by \"-1\"\r\n" );
document.write( "\r\n" );
document.write( "\"%2815%29%2A%28-1%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"-15\"\r\n" );
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document.write( "Edwin
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