Question

The locus of the point w=re(z)+1/z, where |z|=3 in complex plane is circle,parabola,ellipse or hyperbola

Answer 1

Answer:

please refer the attachment

Answer 2

Step-by-step explanation:   W = re(Z) + 1/Z        and |Z| =3  where Z= x+iy

             W= x+1/x+iy     ,now rationalizing

             W=  x+  $\frac{x-iy}{x^{2}+y^{2} }$                                                        ($\frac{1}{x+iy}$  x$\frac{x-iy}{x-iy}$  = $\frac{x-iy}{x^{2} +y^{2} }$ )

but x²+y² = 9         because |z| =3 ⇒ √x²+y² =3 ⇒x²+y² = 9

          w = x+ $\frac{x-iy}{9}$

              = 10x-iy/9

             = $\frac{10x}{9} +(\frac{-iy}{9} )$ correct answer is above instead of given answer