document.write( "Question 420875: [24(cos150+isin150)]/[2(cos30+isin30)] \n" ); document.write( "

Algebra.Com's Answer #293984 by jsmallt9(3759) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%2824%28cos%28150%29%2Bi%2Asin%28150%29%29%29%2F%282%28cos%2830%29%2Bi%2Asin%2830%29%29%29\"$
\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( " $\"%2824%2F2%29%28cos%28150-30%29+%2B+i%2Asin%28150-30%29%29\"$
\n" ); document.write( "which simplifies to
\n" ); document.write( " $\"%2812%29%28cos%28120%29+%2B+i%2Asin%28120%29%29\"$
\n" ); document.write( "which is the answer in polar form. For standard form, a+bi, we replace the cos and sin with their values. 120 is a special angle so we don't need a calculator:
\n" ); document.write( " $\"%2812%29%28%28-1%2F2%29+%2B+i%2Asqrt%283%29%2F2%29\"$
\n" ); document.write( "Distributing the 12 we get:
\n" ); document.write( " $\"-6+%2B+i%2A%286sqrt%283%29%29\"$
\n" ); document.write( "or
\n" ); document.write( " $\"-6+%2B+%286sqrt%283%29%29i\"$ \n" ); document.write( "

\n" );