If `z` and `w` are two complex numbers having non-negative imaginary parts such that `arg((z-2)/(z+2))=arg((w-1)/(w+1))=pi/2` , `|w-z|`< `k;` evaluate `k` .(Here `k` is least upperbound)

If z and w are two complex number such that |zw|=1 and arg(z)arg(w)=(pi)/(2), then show that bar(z)w=-i

Let z_(1),z_(2) be two distinct complex numbers with non-zero real and imaginary parts such that "arg"(z_(1)+z_(2))=pi//2 , then "arg"(z_(1)+bar(z)_(1))-"arg"(z_(2)+bar(z)_(2)) is equal to

If z is purely imaginary ; then arg(z)=+-(pi)/(2)

Let Z and w be two complex number such that |zw|=1 and arg(z)-arg(w)=pi/2 then

If z and w are two complex numbers simultaneously satisfying te equations,z^(3)+w^(5)=0 and z^(2)+bar(w)^(4)=1, then

If z, z_1 and z_2 are complex numbers, prove that (i) arg (barz) = - argz (ii) arg (z_1 z_2) = arg (z_1) + arg (z_2)

Suppose two complex numbers z=a+ib , w=c+id satisfy the equation (z+w)/(z)=(w)/(z+w) . Then

Let z_(1) and z_(2) be two complex numbers such that bar(z)_(1)+bar(iz)_(2)=0 and arg(z_(1)z_(2))=pi then find arg(z_(1))