Proving Complex Numbers are Rational

[halvizo1031]

Homework Statement

Let Z and W be complex numbers. If /Z/ and /W/ are rational and /W-Z/ is rational, then
/(1/Z)-(1/W)/ is rational.

Homework Equations

The Attempt at a Solution

How do I represent Z and W as rational complex numbers?

 

[Fredrik]

z and w are arbitrary complex numbers. Rational numbers can be written in the form a/b, where a and b are integers.

And it's |z|, not /z/.

 

[LCKurtz]

How do I represent Z and W as rational complex numbers?

It isn't Z and W that are rational, it is their magnitudes |Z| and |W|.