document.write( "Question 420876: 3(cos395+isin395)
\n" ); document.write( "-------------------------
\n" ); document.write( "9(cos65+isin65) \n" ); document.write( "
Algebra.Com's Answer #293982 by jsmallt9(3759)\"\" \"About 
You can put this solution on YOUR website!
When posting fractions on Algebra.com, please
  1. Type a \"(\" (left parenthesis)
  2. Type the entire numerator
  3. Type \")/(\" (the right parenthesis closes the numerator, the \"/\" represents the division, and the left parenthesis opens the denominator)
  4. Type the entire denominator
  5. Type a \")\" (to close the denominator)

\n" ); document.write( "This makes the actual fraction easy to understand. When you post fractions the way you did this one, it can be difficult to read.

\n" ); document.write( "Putting arguments of function in parentheses helps, too. So your expression, posted this way, would be:
\n" ); document.write( "(3(cos(395)+isin(395)))/(9(cos(65)+isin(65)))

\n" ); document.write( "\"%283%28cos%28395%29%2Bi%2Asin%28395%29%29%29%2F%289%28cos%2865%29%2Bi%2Asin%2865%29%29%29\"
\n" ); document.write( "Dividing complex numbers written in polar form is fairly simple because there is a formula that makes it easy. For two complex numbers:
\n" ); document.write( "\"z%5B1%5D+=+r%5B1%5D%28cos%28x%5B1%5D%29+%2B+i%2Asin%28x%5B1%5D%29%29\"
\n" ); document.write( "and
\n" ); document.write( "\"z%5B2%5D+=+r%5B2%5D%28cos%28x%5B2%5D%29+%2B+i%2Asin%28x%5B2%5D%29%29\"
\n" ); document.write( "we can divide them using the formula:
\n" ); document.write( " (as long as \"z%5B2%5D\" is not zero).

\n" ); document.write( "Using this formula to divide your complex numbers we get:
\n" ); document.write( "\"%283%2F9%29%28cos%28395-65%29+%2B+i%2Asin%28395-65%29%29\"
\n" ); document.write( "which simplifies to
\n" ); document.write( "\"%281%2F3%29%28cos%28330%29+%2B+i%2Asin%28330%29%29\"
\n" ); document.write( "which is the answer in polar form. For standard form, a+bi, we replace the cos and sin with their values. 330 is a special angle so we don't need a calculator:
\n" ); document.write( "\"%281%2F3%29%28sqrt%283%29%2F2+%2B+i%2A%28-1%2F2%29%29\"
\n" ); document.write( "Distributing the 1/3 we get:
\n" ); document.write( "\"sqrt%283%29%2F6+%2B+i%2A%28-1%2F6%29\"
\n" ); document.write( "or
\n" ); document.write( "\"sqrt%283%29%2F6+%2B+%28-1%2F6%29i\" \n" ); document.write( "
\n" );