If `|z-3i| < sqrt5,` prove that `|i(z+1)+1| < 2 sqrt5.`

If |z-3+i| = 4 then the locus of z = x +iy is

If |z-3+i|=4 , then the locus of z is

If |z-3+i|=4 determine the locus of z.

If |z-3+ i|=4 , then the locus of z is

How many solutions system of equations, arg (z + 3 -2i) = - pi//4 and |z + 4 | - |z - 3i| = 5 has ?

How many solutions system of equations, arg (z + 3 -2i) = - pi/4 and |z + 4 | - |z - 3i| = 5 has ?

If z complex number satisfying |z-3|<=5 then range of |z+3i| is (where i= sqrt(-1) )

show that if |(z-3i)/(z+3i)|=1 then z is a real number.

If z = x + iy and if the point P in the Argand plane represents z , then the locus of P satisfying the equation |z- 3i| + |z + 3i| = 10 is

The region represented by the inequality |2z-3i| lt |3z-2i| is