### 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 ππ, 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 ππ, its conjugate is π minus ππ.

Letβs look at our complex number then. Well, itβs 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. Itβs two plus seven π.