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Question

Let z be a complex number satisfying |2z+10+10i|535. If arg denotes the principal argument lying in (π,π], then the least value of arg(z) is

A
5π6
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B
3π4
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C
3π4
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D
5π6
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Solution

The correct option is A 5π6
|2z+10+10i|535
|z+(5+5i)|5352
This represents interior of a circle whose centre is (5,5) and radius is 52(31).

Here, AB=radius=52(31)
OA=52+52=52
sinθ=52(31)52=3122
θ=15=π12
arg(z) is minimum when z is at B.
XOA=π+tan155=3π4
XOB=XOA+(θ)
=3π4π12=5π6

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