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$If complex number z lies on the curve | z - (- 1 + i) | = 1, then the locus of the complex$
$number ω = \frac{z + i}{1 - i}, i = \sqrt{- 1} is a circle having$

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centre at (−3/2,1/2) and radius 12

centre at (3/2,−1/2) and radius 12

centre at (3/2,−1/2) and radius 2

centre at (−3/2,1/2) and radius 2

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detailed solution

Correct option is A

We have |z−(−1+i)|=1⇒|z+1−i|=1 Now, ω=z+i1−i⇒(1−i)ω=z+iadding -2i+1 on both sides⇒(1−i)ω−2i+1=z+1−i⇒|(1−i)ω−2i+1|=|z+1−i|⇒|1−i|ω+1−2i1−i=1⇒ω+(1−2i)(1+i)(1+i)(1−i)=12⇒ω−−3+i2=12

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If complex number z lies on the curve |z−(−1+i)|=1, then the locus of the complex number ω=z+i1−i,i=−1 is a circle having

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

$If complex number z lies on the curve | z - (- 1 + i) | = 1, then the locus of the complex$
$number ω = \frac{z + i}{1 - i}, i = \sqrt{- 1} is a circle having$