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

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Answer 1 · 2017-02-17T12:48:26

See 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):}#