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Question

Among the complex number z satisfying condition |z+1-i|1,the number having the least positive argument is


A

1-i

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B

-1+i

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C

-i

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D

None of these

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Solution

The correct option is D

None of these


Explanation for the correct option:

Finding the number having the least positive argument:

|z(1+i)|1 represents a region of a circle with centre (1+i) and radius 1. The point on this circle with least amplitude is P(0,1) and corresponds to i.

Given |z+1-i|1...(1)

z=1-i

Substitute in (1)

1i+1i1

Does not satisfy

Put z=1+i in (1)

1+i+1i1

Argument of z=-π4 argz(θ)=tan-1(realpartimaginarypart)

Putz=i

i+1i1

Does not satisfy

Hence, option (D) is the answer.


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