How do you find the values of m and n that make the equation #8+15i=2m+3ni# true?

1 Answer
Jan 6, 2017

Please see below.

Explanation:

Complex numbers are equal exactly when the real parts are equal and the imaginary parts are equal.

#a+bi = c+di# if and only of #a=c# and #b=d#.

So #8+15i = 2m+3ni# if and only if

#8 = 2m# and #15 = 3n#. And this happens only when

#m=4# and #n=5#.

Note Students sometimes wonder why mathematicians bother to state when two complex numbers are equal. After we state it, some react with "Well, obviously!".

But consider another kind of two-part number -- fractions.

When is #a/b=c/d#?

Since #3/6 = 7/14# the answer is NOT only when #a=c# and #b=d#.

(In case you've forgotten, the answer is #a/b=c/d# if and only if #ad=bc#.)