Geometrical Representation of Argument and Modulus
For a complex...
Question
For a complex number z, if |z−1+i|+|z+i|=1, then the range of the principle argument of z is ( Here, principle argument ∈(−π,π])
A
[−π4,π4]
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B
[π4,π2]
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C
[−π2,−π4]
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D
[−π2,π2]
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Solution
The correct option is C[−π2,−π4] |z−1+i|+|z+i|=1 or, |z−(1−i)|+|z−(−i)|=|(1−i)−(−i)| ⇒ Locus of z is the line segment joining −i and 1−i From the above figure, minimum value of arg(z)=−π2 and Maximum value of arg(z)=−π4 ∴ Principle arg(z)∈[−π2,−π4]