Find the complex number z for which `|z+1| = z + 2(1 + i)`.

Find the complex number z for which |z| = z + 1 + 2i.

Find the complex number z such that |z-2+2i| le 1 and z has the : least absoluate value.

Find the complex number z such that |z-2+2i| le 1 and z has the : numerically least amplitude.

Consider the complex number z_1 = 2 - i and z_2 = -2 + i Find (z_1z_2)/z_1 . Hence, find abs((z_1z_2)/z_1)

Consider the complex number z_1 = 2 - i and z_2 = 2 + i Find 1/(z_1z_2) . Hence, prove than I_m(1/(z_1z_2)) = 0

If the complex number z is such that |z-1|le1 and |z-2|=1 find the maximum possible value |z|^(2)

Among the complex numbers z which satisfies |z-25i|<=15, find the complex numbers z having

The number of complex numbers z such that |z - i| = |z + i| = |z + 1| is

Consider the complex number z_1 = 3+i and z_2 = 1+i .What is the conjugate of z_2 ?