If z is any complex number and iz^3+z^2-z+i=0, where i= -1 , then what is the value of (|z|+1)^2?

NDA 2024 Mathematics question

If is any complex number and , where , then what is the value of ?

Answer: (B)

Factorise: iz^3+z^2-z+i = z^2(iz+1)+i(iz+1) = (iz+1)(z^2+i), since . So or $

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Question ID VK-029773