Write the argument of -i.

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Solution

Let z = - i

Here x = 0 and y = -1 < 0,

$∴ θ$ lies in quadrant IV

$∴ θ = a r g (z) = t a n^{- 1} (\frac{- 1}{0}) = t a n^{- 1} (- \infty) = t a n^{- 1} (- t a n \frac{π}{2}) (∵ t a n \frac{π}{2} = \infty) = t a n^{- 1} (t a n (2 π - \frac{π}{2})) (∵ t a n (2 π - θ) = - t a n θ) = 2 π - \frac{π}{2} = \frac{4 π - π}{2} = \frac{3 π}{2}$

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