# How do you find the values of m and n that make the equation (m+1)+3ni=5-9i true?

Dec 30, 2016

$m = 4$ and $n = - 3$

#### Explanation:

Two complex numbers ${a}_{1} + i {b}_{1}$ and ${a}_{2} + i {b}_{2}$ are equal

is ${a}_{1} = {a}_{2}$ and ${b}_{1} = {b}_{2}$

Hence as $\left(m + 1\right) + 3 n i = 5 - 9 i$

$m + 1 = 5$ and $3 n = - 9$

i.e. $m = 5 - 1 = 4$ and $n = - 3$