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Question

If z is a complex number satisfying |z|=1, then the range of arg(11z) is

A
(0,π)
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B
[0,π]
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C
[0,π2]
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D
(π2,π2)
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Solution

The correct option is D (π2,π2)
Let u=11z
z=11u|z|=11u11u=1|u1|=|u|
Locus of u is the perpendicular bisector of the line segment joining points (0,0) and (1,0)
Re(u)=12
Therefore,
arg(u)(π2,π2)

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