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

## 2 Answers

10 years ago

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

10 years ago

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

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