Question Video: Finding the Conjugate of a Complex Number in Algebraic Form Mathematics

What is the conjugate of the complex number 2 β 7π?

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Video Transcript

What is the conjugate of the complex numbers two minus seven π?

We begin by recalling what we actually mean by the complex number π§. This is of the form π plus ππ, where π and π are real constants. We say that π is the real part of π§ whereas π, the coefficient of π, is its imaginary part. We then define the complex conjugate of π§ to be equal to π§ star. And we find this by changing the sign of the imaginary part. And so, for a complex number π plus ππ, its conjugate is π minus ππ.

Letβs look at our complex number then. Well, itβs two minus seven π. The real part of π§ is two. And its imaginary part is negative seven. We said that, to find the conjugate of a complex number, we change the sign of the imaginary part.

So the complex conjugate of π§, π§ star, will have an imaginary part of positive seven. Its real part remains as two. So we find π§ star is equal to two plus seven π. And so, we found the conjugate of the complex number two minus seven π. Itβs two plus seven π.