If |z| = 1, then the point representing thecomplex number - 1 + 3z will lie onA. circle B.straightline c.parabola D. hyperbola

3z represents the circle of radius 3 units centered at the origin.  -1+3z, is the previous circle shifted along the negative real axis by one unit. So the answer is A. circle

let Z=x1+iy1

  mod(z)=1

     (x1)^2 + (y1)^2 =1   .............eq1

 now Z2 =3Z-1        (GIVEN)

       Z2= (3x1-1) + i3y1

 X+IY =3x1 -1 + i3y1

 X=3x1-1......eq2         and     Y=3y1.....eq3

     from eq 1 and 3

        Y^2/9 = 1 - (x1)^2.....eq4

  from eq 2 and 4

      Y^2/9 + (X+1)^2 /9 =1  equation of circle

Approved