Midpoint and distance on complex plane | Imaginary and complex numbers | Precalculus | Khan Academy

TL;DR

Plotting two complex numbers on the complex plane, finding their distance, and identifying the exact midpoint between them.

Transcript

Voiceover:So we have two complex numbers here. The complex number z is equal to two plus three i and the complex number w is equal to negative five minus i. What I want to do in this video is to first plot these two complex numbers on the complex plane and then think about what the distance is between these two numbers on the plane and what complex... Read More

Key Insights

• 🛫 Complex numbers can be plotted on the complex plane using their real and imaginary parts as coordinates.
• ✈️ The distance between two complex numbers on the complex plane can be found using the Pythagorean theorem.
• 🥳 The midpoint between two complex numbers has a real part equal to the mean of their real parts and an imaginary part equal to the mean of their imaginary parts.
• ✈️ The complex plane is a useful tool for visualizing and analyzing complex numbers.
• ✈️ The Pythagorean theorem can be applied to calculate distances on the complex plane.

Questions & Answers

Q: How do you plot complex numbers on the complex plane?

To plot a complex number on the complex plane, you use its real part as the x-coordinate and its imaginary part as the y-coordinate.

Q: What is the formula for finding the distance between two complex numbers on the complex plane?

The distance between two complex numbers can be found using the Pythagorean theorem, where the real difference and imaginary difference are the two legs of a right triangle.

Q: How do you find the midpoint between two complex numbers?

To find the midpoint, you calculate the mean of the real parts and the mean of the imaginary parts of the two complex numbers.

Q: How can you verify the midpoint plotted on the complex plane?

By plotting the calculated midpoint on the complex plane, you can visually confirm if it lies exactly halfway between the two given complex numbers.

Summary & Key Takeaways

• The video explains how to plot two complex numbers, z and w, on the complex plane using their real and imaginary parts.

• The distance between the two complex numbers on the complex plane can be found using the Pythagorean theorem.

• The midpoint between the two complex numbers can be determined by finding the mean of their real parts and imaginary parts.