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