document.write( "Question 205028: Hi. \r
\n" ); document.write( "\n" ); document.write( "Expressed in \"a+%2B+bi\" form, \"5%2F%283+%2B+i%29\" is equivalent to: \r
\n" ); document.write( "\n" ); document.write( "A) \"15+-+5i\", B) \"3%2F2+-+1%2F2\"\"i\", C) \"5%2F3+-+5i\", D) \"15%2F8+-+5%2F8\"\"i\" \n" ); document.write( "
Algebra.Com's Answer #154854 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
Expressed in \"a+%2B+bi\" form, \"5%2F%283+%2B+i%29\" is equivalent to: \r
\n" ); document.write( "\n" ); document.write( "A) 15 - 5i, B) (3/2) - (1/2i), C) (5/3) - 5i, D) (15/8) - (5/8i)
\n" ); document.write( "
\r\n" );
document.write( "\"5%2F%28%283+%2B+i%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Form the conjugate of the denominator by changing the\r\n" );
document.write( "sign of the term containing \"i\".  The conjugate of\r\n" );
document.write( "\"%283%2Bi%29\" is \"%283-i%29\" so we multiply by the fraction\r\n" );
document.write( "\"%28%283-i%29%29%2F%28%283-i%29%29\" which just equals \"1\" and will not\r\n" );
document.write( "change the value:\r\n" );
document.write( "\r\n" );
document.write( "\"5%2F%28%283+%2B+i%29%29\"×\"%28%283-i%29%29%2F%28%283+-+i%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Indicate the multiplication of the tops and bottoms:\r\n" );
document.write( "\r\n" );
document.write( "\"%285%283-i%29%29%2F%28%283%2Bi%29%283-i%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Distribute the top, FOIL out the denominator:\r\n" );
document.write( "\r\n" );
document.write( "\"%285%283-i%29%29%2F%289-3i%2B3i-i%5E2%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%285%283-i%29%29%2F%289-cross%283i%29%2Bcross%283i%29-i%5E2%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%285%283-i%29%29%2F%289-i%5E2%29\"\r\n" );
document.write( "\r\n" );
document.write( "Now we substitute \"%28-1%29\" for \"i%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"%285%283-i%29%29%2F%289-%28-1%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%285%283-i%29%29%2F%289%2B1%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%285%283-i%29%29%2F10\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28cross%285%29%283-i%29%29%2Fcross%2810%5B2%5D%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%283-i%29%2F2\"\r\n" );
document.write( "\r\n" );
document.write( "Make two fractions:\r\n" );
document.write( "\r\n" );
document.write( "\"3%2F2-i%2F2\"\r\n" );
document.write( "\r\n" );
document.write( "Write \"i%2F2\" as \"1%2F2\"\"i\"\r\n" );
document.write( "\r\n" );
document.write( "\"3%2F2-1%2F2\"\"i\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );