# How do you find the values of m and n that make the equation (2m-3n)i+(m+4n)=13+7i true?

Mar 1, 2017

$m = \frac{67}{11} , n = \frac{19}{11}$

#### Explanation:

$\left(2 m - 3 n\right) i + \left(m + 4 n\right) = 13 + 7 i \to \left(2 m - 3 n - 7\right) i + \left(m + 4 n - 13\right) = 0 i + 0$

$\left\{\begin{matrix}2 m - 3 n - 7 = 0 \\ m + 4 n - 13 = 0\end{matrix}\right.$

now solving for $m , n$ we have

$m = \frac{67}{11} , n = \frac{19}{11}$