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Point P represents the complex num,ber z...

Point P represents the complex num,ber `z=x+iy` and point Q the complex num,ber `z+ 1/z`. Show that if P mioves on the circle `|z|=2` then Q oves on the ellipse `x^2/25+y^2/9=1/9`. If z is a complex such that `|z|=2` show that the locus of `z+1/z` is an ellipse.

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