### Video Transcript

Let π§ one, π, and π§ two be
complex numbers such that π lies at the midpoint of the line segment connecting π§
one to π§ two. Given that π§ two equals four plus
five π and π equals negative 12 plus 20π, find π§ one.

Well, we could draw an Argand
diagram and reason geometrically. But thereβs another way. We know that the midpoint π is the
arithmetic mean of the complex numbers π§ one and π§ two. And we can rearrange this equation
to find π§ one in terms of π and π§ two. We multiply both sides by two,
subtract π§ two from both sides, and swap the sides to find that π§ one is two π
minus π§ two. We know the values of π and π§
two. And so we substitute them. We distribute the two and the minus
sign and simplify to find that π§ one is negative 28 plus 35π.