Mathematical problem solving, complex number Given z = (2m square + 3m-2) + (m square + m-2) I (M belongs to R) When z = 0, find the value of M

Mathematical problem solving, complex number Given z = (2m square + 3m-2) + (m square + m-2) I (M belongs to R) When z = 0, find the value of M

When z = 0, then the square of 2m + 3m-2 = 0 and the square of M + m-2 = 0
From the square of 2m + 3m-2 = 0, M = - 2 or M = 1 / 2
From the square of M + m-2 = 0, M = - 2 or M = 1
So m = - 2