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Question

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) y−axis
(d) none of these


Solution

z+1=1z+12=12z+1z+1¯=1z+1z¯+1=1zz¯+z+z¯+1=1zz¯+z+z¯=0Since, z=x+iyzz¯+z+z¯=0x+iyx-iy+x+iy+x-iy=0x2+y2+2x=0x+12+y-02=12which is the equation of a circle with centre (-1, 0) and radius 1

Hence, the correct option is (b).

Mathematics
RD Sharma XI (2019)
All

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