Let `z (ne 2)` be a complex number such that `log_(1//2) |z-2| gt log_(1//2)|z|`. Then prove that Re `(z) gt 1`.

If z is a complex number such that Re (z) = Im (z), then :

If z is a complex number such that z+ |z|=8 +12i then the value of |z^2| is

If z_(1) and z_(2) are complex numbers such that z_(1) ne z_(2) and |z_(1)|= |z_(2)| . If z_(1) has positive real part and z_(2) has negative imaginary part, then ((z_(1) +z_(2)))/((z_(1)-z_(2))) may be

If z_(1) and z_(2) are two non-zero complex numbers such that |z_(1) + z_(2)| = |z_(1)| + |z_(2)| , then arg ((z_(1))/(z_(2))) is equal to a)0 b) -pi c) -(pi)/(2) d) (pi)/(2)

Let z_(1) and z_(2) be complex numbers satisfying |z_(1)|=|z_(2)|=2 and |z_(1)+z_(2)|=3 . Then |(1)/(z_(1))+(1)/(z_(2))|=

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=x+iy is a complex number such that |z|=Re(iz)+1 , then the locus of z is

If the conjugate of a complex number z is (1)/(i-1) , then z is

Let w ne pm 1 be a complex number. If |w| =1 and z = (w -1)/(w +1), then R (z) is equal to