If z is a complex number such that −π2≤arg(z)≤π2, then which of the following inequality is always true?
A
|z−¯z|≤|z|(arg z - arg¯z)
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B
|z−¯z|≥|z|(arg z - arg¯z)
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C
|z−¯z|=|z|(arg z - arg¯z)
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D
None of these
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Solution
The correct option is A|z−¯z|≤|z|(arg z - arg¯z)
From the above diagram, |z−¯z| is length of chord AB while |z|(arg z - arg¯z) is arc length AB. ∴|z−¯z|≤|z|(arg z - arg¯z)