" :24Find 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 = 3+i and z_2 = 1+i .Find 1/z_2

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

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

Consider the complex number z_1 = 3+i and z_2 = 1+i .Using the value of 1/z_2 , find (z_1)/z_2