The question already has a zero and a pole in the complex plane. It is asking to add additional zero and pole so LTI becomes zero valued.
zeros=-1/2 + 1/2 i , poles = -1/3 -1/3 i .
What I understand from it is that we have to make sure that in the end transfer function, there are no complex parts (there is no iota).. that would be real valued... but then why are these zeros and poles not in conjugate pairs? If they are in conjugate then it is already real valued .... so is the question there to confuse us or what? If I am missing something very basic please mention it so I can learn it.
Thank you. !