Find the locus of the complex number, `Z = x + iy`
given, `|(x+iy-2i)/(x+iy+2i)|= sqrt(2)`

Find the locus of a complex number, z=x +iy , satisfying the relation |(z-3i)/(z+3i)| le sqrt(2) . Illustrate the locus of z in the Argand plane.

Find the locus of the complex number z=x+iy , satisfying relations arg(z-1)=(pi)/(4) and |z-2-3i|=2 .

Find the following as a single complex number x+ iy = (5+i9) (-3+ i4)

Find the locus of a complex number z=x +yi , satisfying the relation |z +i|=|z+ 2| . Illustrate the locus of z in the Argand plane

Find the locus of a complex number z= x + yi , satisfying the relation |2z+ 3i| ge |2z + 5| . Illustrate the locus in the Argand plane.

If at least one value of the complex number z=x+iy satisfies the condition |z+sqrt(2)|=sqrt(a^(2)-3a+2) and the inequality |z+isqrt(2)| lt a , then

Find the following as a single complex number x+ iy (sqrt(6)+i5)(sqrt(6)-i(1)/(5))

Find the values of x and y if 2x+4iy = -i^(3)x-y+3

Point P represents the complex num,ber z=x+iy and point Q the complex num,ber z+ 1/z . Show that if P mioves on the circle |z|=2 then Q oves on the ellipse x^2/25+y^2/9=1/9 . If z is a complex such that |z|=2 show that the locus of z+1/z is an ellipse.

Find the real numbers x,y such that ( iy+ x)(3+2i) = 1+ i