explain step wise don't skip any step !! Q 4 If lm2z+1iz+1=-2, then the locus of the - Maths - Complex Numbers and Quadratic Equations

Question

explain step wise don't skip any step !!
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

Koka Sri Lakshmi Divya Sai · Accepted Answer

Dear Student

GivenIm2z+1iz+1=-2Let z=x+iy⇒2x+iy+1ix+iy+1⇒2x+2iy+1xi-y+1×(1-y)-ix(1-y)-ix⇒2x-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-2x2⇒2y-x=4y-2⇒x+2y=2Which is a straight line
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explain step wise...don't skip any step !! 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

explain step wise...don't skip any step !!
Q.4. If $l m (\frac{2 z + 1}{i z + 1}) = - 2$ , 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