The complex number Z = M2-1 + (m2-m-2) I is: (1) real number; (2) imaginary number; (3) pure imaginary number

The complex number Z = M2-1 + (m2-m-2) I is: (1) real number; (2) imaginary number; (3) pure imaginary number

(1) ∵ complex z = M2-1 + (m2-m-2) I is a real number, ∵ m2-m-2 = 0, ∵ M = - 1. M = 2 (2) complex z = M2-1 + (m2-m-2) I is an imaginary number, ∵ m2-m-2 ≠ 0 ∵ m ≠ - 1. M ≠ 2 (3) complex Z = M2-1 + (M2 + 3M + 2) I is a pure imaginary number ∵ m2-m-2 ≠ 0 and M2-1 = 0 ∵ M = 1