document.write( "Question 420873: [16(cos300+isin300)]/[8(cos60+isin60)] \n" ); document.write( "

Algebra.Com's Answer #293988 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%2816%28cos%28300%29%2Bi%2Asin%28300%29%29%29%2F%288%28cos%2860%29%2Bi%2Asin%2860%29%29%29\"$
\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( " $\"%2816%2F8%29%28cos%28300-60%29+%2B+i%2Asin%28300-60%29%29\"$
\n" ); document.write( "which simplifies to
\n" ); document.write( " $\"%282%29%28cos%28240%29+%2B+i%2Asin%28240%29%29\"$
\n" ); document.write( "which is the answer in polar form. For standard form, a+bi, we replace the cos and sin with their values. 240 is a special angle so we don't need a calculator:
\n" ); document.write( " $\"%282%29%28%28-1%2F2%29+%2B+i%2A%28-sqrt%283%29%2F2%29%29\"$
\n" ); document.write( "Distributing the 2 we get:
\n" ); document.write( " $\"-1+%2B+i%2A%28-sqrt%283%29%29\"$
\n" ); document.write( "or
\n" ); document.write( " $\"-1+%2B+%28-sqrt%283%29%29i\"$ \n" ); document.write( "

\n" );