Question Video: Identifying When Two Complex Numbers Are Equal | Nagwa Question Video: Identifying When Two Complex Numbers Are Equal | Nagwa

# Question Video: Identifying When Two Complex Numbers Are Equal Mathematics • First Year of Secondary School

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If the complex numbers 7 + ππ and π β 3π are equal, what are the values of π and π?

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### Video Transcript

If the complex numbers seven plus ππ 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.

Letβs have a look at the complex numbers seven plus ππ 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 ππ and π minus three π to be equal, π must be equal to negative three and π must be equal to seven.

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