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Question
If the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on ______.
Options
X-axis
Circle with centre (1, 0) and radius 1
Circle with centre (–1, 0) and radius 1
Y-axis
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Solution
If the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on circle with centre (–1, 0) and radius 1.
Explanation:
|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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