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Complex Numbers question

2019 · Shift 1 · Q19

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PYQ Library
JEE Advanced
Mathematics
Complex Numbers
2019 · Shift 1 · Q19

Complex Numbers question

2019 · Shift 1 · Q19

JEE AdvancedMathematicsComplex NumbersMCQ+3 / −1

Let S be the set of all complex numbers z satisfying

\left| {z - 2 + i} \right| \ge \sqrt 5

. If the complex number z0 is such that

{1 \over {\left| {{z_0} - 1} \right|}}

is the maximum of the set

\left\{ {{1 \over {\left| {{z_0} - 1} \right|}}:z \in S} \right\}

, then the principal argument of

{{4 - {z_0} - {{\overline z }_0}} \over {{z_0} - {{\overline z }_0} + 2i}}

is

A
${\pi \over 4}$
B
${3\pi \over 4}$
C
$- {\pi \over 2}$
D
${\pi \over 2}$

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