document.write( "Question 1062350: Given the equivalent impedance of a circuit can be calculated by the expression
\n" ); document.write( " Z=(Z1*Z2)/(Z1+Z2)
\n" ); document.write( " If Z1 = 1+j5 and Z2 = 12+j3, calculate the impedance Z in both rectangular and polar forms \n" ); document.write( "

Algebra.Com's Answer #677238 by math_helper(2461) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+Z+=+Z1%2AZ2%2F+%28Z1%2BZ2%29+\"$ =
\n" ); document.write( " $\"+%281%2Bj5%29%2812%2Bj3%29+%2F+%281%2Bj5%2B12%2Bj3%29+\"$ =
\n" ); document.write( " $\"+%2812%2Bj3%2Bj60%2Bj%5E2%2815%29%29+%2F+%2813%2Bj8%29+\"$ =
\n" ); document.write( " $\"+%28-3%2Bj63%29%2F%2813%2Bj8%29+\"$ =
\n" ); document.write( " $\"+%28-3%2Bj63%29%2A%2813-j8%29+%2F+%28%2813%2Bj8%29%2A%2813-j8%29%29+\"$ =
\n" ); document.write( " $\"+%28-39%2Bj24%2Bj819-j%5E2%28504%29%29+%2F+%28169-j%5E2%2864%29%29+\"$ =
\n" ); document.write( " $\"++%28465%2Bj843%29+%2F+%28233%29+\"$ (rectangular form with integers) =
\n" ); document.write( " $\"++Z+=+1.9957+%2B+j3.618+\"$ (rectangular form)\r
\n" ); document.write( "\n" ); document.write( "—
\n" ); document.write( "Polar form: $\"+r=sqrt%281.9957%5E2%2B3.618%5E2%29+=+4.1319+\"$
\n" ); document.write( " $\"+theta+=+arccos%281.9957%2F4.1319%29+=+61.12%5Eo+\"$
\n" ); document.write( " $\"+Z+=+4.1319+\"$ /_ $\"+61.12%5Eo+\"$ (polar form, where /_ means \"at angle\")
\n" ); document.write( "
\n" ); document.write( "—
\n" ); document.write( "For reference Z = r/_theta = r*e^(j*theta) = r*(cos (theta) + j*sin (theta))\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );