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Q.4. If l m 2 z + 1 i z + 1 = - 2 , then the locus of the point representing z in the complex plane is
(a) a circle
(b) a straight line
(c) a parabola
(d) None of these

Dear Student

GivenIm2z+1iz+1=-2Let z=x+iy2x+iy+1ix+iy+12x+2iy+1xi-y+1×(1-y)-ix(1-y)-ix2x-2xy-i2x2+2iy-2iy2+2xy+1-y-ix1-y2+x2GivenIm2z+1iz+1=-2-2x2+2y-2y2-x1-y2+x2=-2-2x2+2y-2y2-x=-21-y2+x2-2x2+2y-2y2-x=-21+y2-2y+x2-2x2+2y-2y2-x=-2-2y2+4y-2x22y-x=4y-2x+2y=2Which is a straight line.

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