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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


Grade:12

2 Answers

Chetan Mandayam Nayakar
312 Points
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

vikas askiitian expert
509 Points
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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