SOLUTION: The complex numbers {{{ z[1] }}} and {{{ z[2] }}} are connected by the relation {{{ z[1] = z[2] + 1/z[2] }}} If the point representing {{{ z[2] }}} in the Argand diagram describe

Question 1161851: The complex numbers and are connected by the relation

If the point representing in the Argand diagram describes a circle of radius and centre at the origin, show that the point representing describes the ellipse

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
There must be an easier, much more elegant way, but this works:

describes the circle of radius

The point representing has
or
Then,

and
meaning that
Similarly,

and
meaning that
Adding up the equations highlighted above,

meaning that

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