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If 0 le "arg"(z) le pi/4, then the least...

If `0 le "arg"(z) le pi/4`, then the least value of `|z-i|`, is

A

1

B

`1/sqrt(2)`

C

`sqrt(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Clearly, `0 le "arg"(z) le pi/4` represents the region in the Argand plane lying in the first quadrant bounded by the x-axis and the line `y=x`. So, `|z-i|` is least if z is the foot of the perpendicular drawn from (0,1) on the line `y=x` and the least value of `|z-i|` is `1/sqrt(2)`.
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