Question Video: Finding a Complex Number given Another Complex Number and the Midpoint between the Two | Nagwa Question Video: Finding a Complex Number given Another Complex Number and the Midpoint between the Two | Nagwa

# Question Video: Finding a Complex Number given Another Complex Number and the Midpoint between the Two Mathematics

Let π§β, π, and π§β be complex numbers such that π lies at the midpoint of the line segment connecting π§β to π§β. Given that π§β = 4 + 5π and π = β12 + 20π, find π§β.

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### 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 thereβs 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.

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