Find the minimum vlaue of `|z-1|` if `||z-3|- |z+1||=2`

If z= (3+7i) (p+iq) , where p, q in Z- {0} , is purely imaginary, then minimum value of |z|^(2) is

The locus z if Re (z+1)= |z-1| is

If |z - (3)/(z)| = 2 , then the greatest value of |z| is a)1 b)2 c)3 d)4

If |z|=1 and z ne +- 1 , then one of the possible values of arg(z)- arg (z+1)- arg (z-1) , is

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)

If z ^(2) + z + 1 = 0, where z is a complex number, then the value of (z + (1)/(z)) ^(2) + (z ^(2) + (1)/( z ^(2))) ^(2) + (z ^(3) + (1)/(z ^(3))) ^(2) +...( z ^(6) + (1)/(z ^(6)) )^(2) is

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 z_(1), z_(2),……..,z_(n) are complex numbers such that |z_(1)| = |z_(2)| = …….. = |z_(n)| = 1 , then |z_(1) + z_(2) +……..+ z_(n)| is equal to a) |z_(1)z_(2)z_(3)…..z_(n)| b) |z_(1)|+|z_(2)|+…….+|z_(n)| c) |(1)/(z_(1)) + (1)/(z_(2)) + ……….+ (1)/(z_(n))| d)n

If |z_(1) + z_(2)|=|z_(1)-z_(2)| , then the difference in the amplitudes of z_(1) and z_(2) is