document.write( "Question 1005850: Write the result in the form a + bi. 3/6+i \n" ); document.write( "
Algebra.Com's Answer #621990 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Please note that 3/6+i means \"3%2F6%2Bi\", not \"3%2F%286%2Bi%29\"\r\n" );
document.write( "You MUST put parentheses around any numerator or denominator\r\n" );
document.write( "which contains more than one number or one letter to tell\r\n" );
document.write( "where it starts and ends.  I am quite sure you meant \"3%2F%286%2Bi%29\"\r\n" );
document.write( "and not \"3%2F6%2Bi\".  You should have typed 3/(6+i). \r\n" );
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document.write( "\"3%2F%286%2Bi%29\"\r\n" );
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document.write( "Multiply by the conjugate of the denominator\r\n" );
document.write( "written over itself:\r\n" );
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document.write( "\"3%2F%286%2Bi%29\"\"%22%D7%22\"\"%286-i%29%2F%286-i%29\"\r\n" );
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document.write( "Indicate the multiplication of the numerators and denominators:\r\n" );
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document.write( "\"%283%286-i%29%29%2F%28%286%2Bi%29%286-i%29%29\"\r\n" );
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document.write( "Distribute the top and FOIL the bottom:\r\n" );
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document.write( "\"%2818-i%29%2F%2836-6i%2B6i-i%5E2%29\"\r\n" );
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document.write( "Cancel the middle terms in the bottom:\r\n" );
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document.write( "\"%2818-i%29%2F%2836-cross%286i%29%2Bcross%286i%29-i%5E2%29\"\r\n" );
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document.write( "\"%2818-i%29%2F%2836-i%5E2%29\"\r\n" );
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document.write( "Since \"i%5E2=-1\" substitute (-1) for i2.\r\n" );
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document.write( "\"%2818-i%29%2F%2836-%28-1%29%29\"\r\n" );
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document.write( "Simplify the denominator:\r\n" );
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document.write( "\"%2818-i%29%2F%2836%2B1%29\"\r\n" );
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document.write( "\"%2818-i%29%2F37\"\r\n" );
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document.write( "Write as two fractions:\r\n" );
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document.write( "\"18%2F37-i%2F37\"\r\n" );
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document.write( "Change the division of i by 37 as a multiplication\r\n" );
document.write( "of the reciprocal of 37, which is \"1%2F37\" by i:\r\n" );
document.write( "\"18%2F37-expr%281%2F37%29i\"\r\n" );
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document.write( "-------------------------------\r\n" );
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document.write( "Here's an easy way if you have a TI-83 or TI-84:\r\n" );
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document.write( "Make sure the calculator is in the mode to take\r\n" );
document.write( "complex numbers.  You can leave it set that way\r\n" );
document.write( "permanently, since it doesn't affect any of the\r\n" );
document.write( "other functions.  Press \"MODE\", scroll down to\r\n" );
document.write( "\"REAL\". Press the right arrow once to put the cursor\r\n" );
document.write( "on \"a+bi\" and press \"ENTER\", then press \"2ND\" \"MODE\".\r\n" );
document.write( "Now it is set to take complex numbers.  You'll never\r\n" );
document.write( "have to do that again.  The reason the TI company\r\n" );
document.write( "doesn't put it in that mode at the factory is because\r\n" );
document.write( "some people, like engineers, have hundreds and hundreds\r\n" );
document.write( "of stored programs in their calculator and the \"a+bi\" \r\n" );
document.write( "mode takes up a little more memory that those people\r\n" );
document.write( "might need for their programs. \r\n" );
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document.write( "Now\r\n" );
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document.write( "Press CLEAR\r\n" );
document.write( "Press 3/(6+i)   <-- the \"i\" is \"2ND\" then the decimal key. \r\n" );
document.write( "                  (the period or decimal key which is the \r\n" );
document.write( "                  middle key at the bottom of the keyboard)\r\n" );
document.write( "                  Be sure to put those parentheses around\r\n" );
document.write( "                  that denominator as you mistakenly forgot \r\n" );
document.write( "                  them above.\r\n" );
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document.write( "Press 2ND ENTER ENTER \r\n" );
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document.write( "read 18/37-34/37i\r\n" );
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document.write( "Edwin
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