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If the complex number z = x + iy satisfies the condition |z +1| = 1 , then z lies on

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If the complex number z = x + iy satisfies the condition |z +1| = 1 , then z lies on

(A) x-axis

(B) circle with centre (1, 0) and radius 1

(C) circle with centre (–1, 0) and radius 1

(D) y-axis

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1 Answer

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Answer is (C),

|z +1|=1 ⇒ |(x +1)+iy| = 1

⇒ (x +1)2 + y2 = 1

which is a circle with centre (–1, 0) and radius 1.

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