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Question

If z0,z1 represents points P,Q on the locus |z1|=1 and the line segment PQ subtends an angle π2 at the point z=1 then z1 is equal to

A
1+i(z01)
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B
i(z01)
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C
1i(z01)
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D
i(z01)
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Solution

The correct options are
A 1+i(z01)
C 1i(z01)
Now
|z1|=1 Represents a circle centered at x=1 y=0 and has a radius of 1.

Now

PQ subtends an angle of π2 at z=1+0i

Hence

z1zz0z=(1).eiπ2=i

z11=(z01)i

z1=1+i(z01)

Similarly if

z01z11=i

z11z01=i

z11=i(z01)

z1=1i(z01)

204324_133788_ans_780fe0a31c814570ae6268926460ed13.jpg

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