If m and n are real numbers, i^2=-1, and (m-n)-4i=7+ni, what is the value of m?
(m-n)-4i=7+ni
m = 7 + ni + n + 4i
To find the value of m, we will equate the real parts and imaginary parts of the given equation.
Given equation: (m - n) - 4i = 7 + ni
Equating the real parts:
m - n = 7
Equating the imaginary parts:
-4i = ni
Since the imaginary parts are equal, we can equate the coefficients of i:
-4 = n
Now, substituting n = -4 into the equation m - n = 7, we can solve for m:
m - (-4) = 7
m + 4 = 7
m = 7 - 4
m = 3
Therefore, the value of m is 3.