If \( \left|z+\frac{1}{z}\right|=1 \); prove that for maximum \( |z|, z \) is purely imaginary.

If \( \left|z+\frac{1}{z}\right|=1 \); prove that for maximum \( |z|, z \) is purely imaginary.

Guys can you do this question using triangle inequality.

If \( \left|z+\frac{1}{z}\right|=1 \); prove that for maximum \( |z|, z \) is purely imaginary.

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