Let z be a complex number. Let w=z+\frac{1}{z}. Show that \left|w^2-3\right|>\left|w\right|^2-3. LHS = \left|z^2+2+\frac{1}{z^2}-3\right| = \left|2cos\left(2\theta \right)-1\right| = 4cos^2x-2-1 = \left(2cos\theta \right)^2-3 RHS = \left|z+\frac{1}{z}\right|^2-3 = \left(2cos\theta \right)^2-3 which is false... where did I go wrong? Thanks for help :)
