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Question

The complex number z which satisfies the condition i+zi-z=1 lies on

(a) circle x2 + y2 = 1
(b) the x−axis
(c) the y−axis
(d) the line x + y = 1


Solution

i+zi-z=1i+zi-z2=12i+zi-zi+zi-z¯=1i+zi-z-i+z¯-i-z¯=1-i2-zi+z¯i+zz¯-i2+zi-z¯i+zz¯=1-i2-zi+z¯i+zz¯=-i2+zi-z¯i+zz¯-zi+z¯i=zi-z¯iz¯i+z¯i=zi+zi2z¯i=2ziz¯=zz is purely real

Hence, the correct option is (b).

Mathematics
RD Sharma XI (2019)
All

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