document.write( "Question 1161851: The complex numbers \"+z%5B1%5D+\" and \"+z%5B2%5D+\" are connected by the relation
\n" ); document.write( "\"+z%5B1%5D+=+z%5B2%5D+%2B+1%2Fz%5B2%5D+\"
\n" ); document.write( "If the point representing \"+z%5B2%5D+\" in the Argand diagram describes a circle of radius \"+a+\" and centre at the origin, show that the point representing \"+z%5B1%5D+\" describes the ellipse
\n" ); document.write( "\"+x%5E2%2F%281%2Ba%5E2%29%5E2+%2B+y%5E2%2F%281-a%5E2%29%5E2+=+1%2Fa%5E2+\"
\n" ); document.write( "

Algebra.Com's Answer #786129 by KMST(5328)\"\" \"About 
You can put this solution on YOUR website!
There must be an easier, much more elegant way, but this works:
\n" ); document.write( "
\n" ); document.write( "\"z%5B2%5D=a%28cos%28theta%29%2Bi%2Asin%28theta%29%29\" describes the circle of radius \"a\"
\n" ); document.write( "
\n" ); document.write( "\"z%5B1%5D=z%5B2%5D%2B1%2Fz%5B2%5D\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "The point representing \"z%5B1%5D=x%2Bi%2Ay\" has
\n" ); document.write( "or
\n" ); document.write( "Then,
\n" ); document.write( "\"x%2F%281%2Ba%5E2%29\"\"%22=%22\"
\n" ); document.write( "and
\n" ); document.write( " meaning that \"highlight%28x%5E2%2F%281%2Ba%5E2%29%5E2=%281%2Fa%5E2%29%2Acos%5E2%28theta%29%29\"
\n" ); document.write( "Similarly,
\n" ); document.write( "\"y%2F%281-a%5E2%29\"\"%22=%22\"
\n" ); document.write( "and
\n" ); document.write( " meaning that \"highlight%28y%5E2%2F%281-a%5E2%29%5E2=%281%2Fa%5E2%29%2Asin%5E2%28theta%29%29\"
\n" ); document.write( "Adding up the equations highlighted above,
\n" ); document.write( "
\n" ); document.write( "meaning that
\n" ); document.write( "\"highlight%28x%5E2%2F%281%2Ba%5E2%29%5E2%2By%5E2%2F%281-a%5E2%29%5E2=1%2Fa%5E2%29\"
\n" ); document.write( "
\n" );