Question

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

Answer 1

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:

`{(2n-5=3),(-m-2=-7):}`

From the first equation we can calculate that:

`2n-5=3 => 2n=8 =>n=4`

The second equation leads to:

`-m-2=-7=>-m=-5=>m=5`

Answer: The two numbers are equal for: `{(m=5),(n=4):}`