# How do you find the values of m and n that make the equation (2n-5)+(-m-2)i=3-7i?

Feb 17, 2017

See explanation.

#### Explanation:

Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal.

In the given example this leads to a system of equations:

$\left\{\begin{matrix}2 n - 5 = 3 \\ - m - 2 = - 7\end{matrix}\right.$

From the first equation we can calculate that:

$2 n - 5 = 3 \implies 2 n = 8 \implies n = 4$

$- m - 2 = - 7 \implies - m = - 5 \implies m = 5$

Answer: The two numbers are equal for: $\left\{\begin{matrix}m = 5 \\ n = 4\end{matrix}\right.$