z=-2m+3mi-9i+4, m is a real number and i^2 = 1, find the value of m 1. z is a real number. 2. z is a purely imaginary number?

1.
z = -2m + 3mi - 9i + 4
z = ( - 2m + 4) + (3m - 9)i

When z is a real number :
The imaginary part = 0
(3m - 9)i = 0
3m - 9 = 0
m = 3


2.
When z is a purely imaginary number :
The real part = 0
-2m + 4 = 0
m = 2

z=-2m+3mi-9i+4
1.
z is a real number
3m-9=0
m=3

2.
z is a purely imaginary number
-2m+4=0
m=2