When m is a real number, z = (1 + I) M & sup2; + (5-2i) m + (6-15i) is a real number, an imaginary number and a pure imaginary number

When m is a real number, z = (1 + I) M & sup2; + (5-2i) m + (6-15i) is a real number, an imaginary number and a pure imaginary number

z=(m²-2m-15)i+m²+5m+6
M & # 178; - 2m + 15 = 0 and M & # 178; - 5m + 6 ≠ 0, M = 5 is a real number
M & # 178; - 2m + 15 ≠ 0, m ≠ 5 and m ≠ - 3 are imaginary numbers
M & # 178; - 2m + 15 ≠ 0 and M & # 178; - 5m + 6 = 0, M = - 2 is a pure imaginary number