### Video Transcript

If the complex numbers seven plus
ππ and π minus three π are equal, what are the values of π and π?

Remember, for two complex numbers
to be equal, their real parts must be equal and their imaginary parts must also be
equal. And the beauty of this fact is it
takes a problem about complex numbers and makes it purely about real numbers, since
both the real parts and imaginary parts of each complex number must be real
numbers.

Letβs have a look at the complex
numbers seven plus ππ and π minus three π then. The real part of the first complex
number is seven, and the real part of our second complex number is π. The imaginary part of our first
complex number is π, and the imaginary part of our second complex number is
negative three. It follows then that seven must be
equal to π and π must be equal to negative three. Both negative three and seven are
real numbers, which satisfies our criteria for the real and imaginary parts of a
complex number. So for the complex numbers seven
plus ππ and π minus three π to be equal, π must be equal to negative three and
π must be equal to seven.