The principal amplitude of $(2 - i) (1 - 2 i)^{2}$ is in the interval

(0, \frac{π}{2})

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(- \frac{π}{2}, 0)

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(- π, - \frac{π}{2})

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(- \frac{π}{2}, \frac{π}{2})

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Solution

The correct option is C $(- π, - \frac{π}{2})$
$(2 - i) (1 - 2 i)^{2}$
$= (2 - i) (- 3 - 4 i)$
$= - 10 - 5 i$
This lies in the third quadrant. Hence, option C is correct.

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