# How do you find the values of m and n that make the equation (2m+5)+(1-n)i=-2+4i true?

Nov 23, 2016

$m = - \frac{7}{2} , n = - 3$

#### Explanation:

For the 2 complex numbers to be equal, the coefficients of the real parts and the imaginary parts must be equal.

$\Rightarrow 2 m + 5 = - 2 \text{ and } 1 - n = 4$

solve: $2 m + 5 = - 2 \Rightarrow m = - \frac{7}{2}$

solve : $1 - n = 4 \Rightarrow n = - 3$

Check.

$\Rightarrow \left(2 \times - \frac{7}{2}\right) + 5 = - 7 + 5 = - 2$

and $1 - \left(- 3\right) = 4$