Complex NumbersHard
Question
If complex number z satisfy 
& |arg(z - 1 - i) = 
, then -
& |arg(z - 1 - i) = , then - Options
A.|z|max = 1 + √2
B.|z|min = √3
C.maximum value of amp(z) is
D.minimum value of amp(z) is - cot-1 √2
- cot-1 √2Solution
|z|max = OA = √2 + 1
|z|min = OB =
= √3
maximum value of amp(z) is corresponding to point A i.e.
minimum value of amp(z) is corresponding to point B i.e - θ = - tan-1 
(∵ tan θ = in triangle OPB)
|z|min = OB =
= √3 maximum value of amp(z) is corresponding to point A i.e.
minimum value of amp(z) is corresponding to point B i.e
- θ = - tan-1 (∵ tan θ =
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