Let `z=1+ai` be a complex number, `a > 0`,such that `z^3` is a real number. Then the sum `1+z+z^2+...+ z^11` is equal to:

Similar Questions

Explore conceptually related problems

Let z!=i be any complex number such that (z-i)/(z+i) is a purely imaginary number. Then z+ 1/z is

Let z be a complex number such that |z| + z = 3 + i (Where i=sqrt(-1)) Then ,|z| is equal to

Let z_1 and z_2 be two complex numbers such that z_1+z_2 and z_1z_2 both are real, theb

Let z be a complex number such that |z|+z=3+I (Where i=sqrt(-1)) Then ,|z| is equal to

Let z be a complex number such that |(z-5i)/(z+5i)|=1 , then show that z is purely real

Z is a complex number such that z+(1)/(z)=2cos3^(0), then the value of z^(2000)+(1)/(z^(2000)) is equal to

If z is a complex number such that |z|=1, z ne 1 , then the real part of |(z-1)/(z+1)| is