If z is a complex number such that −π$$/2$$≤ arg⁡z≤π$$/2$$ then which of the following inequality is true.

Correct option is 1|z−z|≤|z||arg⁡(z)−arg⁡(z)|

Questions

If $z$ is a complex number such that $- π / 2 \leq$ $\arg z \leq π / 2$ then which of the following inequality is true.

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|z−z|≤|z||arg⁡(z)−arg⁡(z)|

|z−z|≤|arg⁡(z)−arg⁡(z)|

|z−z|>|z||arg⁡(z)−arg⁡(z)|

None of these

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detailed solution

Correct option is A

z|z|−z¯|z|≤|arg⁡(z)−arg⁡(z¯)|⇒|z−z¯|≤|z||arg⁡(z)−arg⁡(z¯)|

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If z is a complex number such that −π/2≤ arg⁡z≤π/2 then which of the following inequality is true.

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If $z$ is a complex number such that $- π / 2 \leq$ $\arg z \leq π / 2$ then which of the following inequality is true.