document.write( "Question 41215: What is the answer of (3-2i)/(7-6i) in standard form. Thank you \n" ); document.write( "
Algebra.Com's Answer #26639 by zeynep(43)\"\" \"About 
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To write (3-2i)/(7-6i) in standard form, we will make the denominator a real number.\r
\n" ); document.write( "\n" ); document.write( "To make the denominator a real number, we multiply it by its conjugate which is (7+6i).\r
\n" ); document.write( "\n" ); document.write( "However we will also multiply the numerator by (7+6i) in order not to change the fraction.(Keep in mind that as long as you multiply the numerator and denominator by the exact the same thing, the fractions will be equivalent.)\r
\n" ); document.write( "\n" ); document.write( "So,
\n" ); document.write( "(3-2i)/(7-6i)=(3-2i).(7+6i)/(7-6i).(7+6i)\r
\n" ); document.write( "\n" ); document.write( "Now let's do the multiplications;\r
\n" ); document.write( "\n" ); document.write( "(3-2i).(7+6i)=21+18i-14i-12i^2 = 21+4i-12.(-1)(Here we used that i^2=-1)\r
\n" ); document.write( "\n" ); document.write( "21+4i-12.(-1)=21+4i+12=33+4i (This is the numerator)\r
\n" ); document.write( "\n" ); document.write( "Now let's find the denominator;
\n" ); document.write( "When you multiply comlex conjugates together you get:
\n" ); document.write( "(a-bi)(a+bi)=a^2+b^2\r
\n" ); document.write( "\n" ); document.write( "so,\r
\n" ); document.write( "\n" ); document.write( "(7-6i).(7+6i)= 7^2+6^2= 49+36=85 (This is the denominator)\r
\n" ); document.write( "\n" ); document.write( "So the standard from of (3-2i)/(7-6i) is;\r
\n" ); document.write( "\n" ); document.write( "(3-2i)/(7-6i)=(3-2i).(7+6i)/(7-6i).(7+6i)= 33+4i /85\r
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