• Understand the difference between imaginary numbers and complex numbers
• Learn how to plot a complex number on a special graph called the complex plane
• Do math operations with complex numbers, and learn how these operations can be shown as scaling or rotation
• Create a series of numbers that are made by repeating a rule, and learn how to find specific terms in the series
• Determine whether a complex number is part of a special set of numbers called the Mandelbrot Set

Navigating Complex Waters

 

Imagine you are a navigator in the age of exploration, charting new territories and plotting courses through unfamiliar waters. The seas you’re sailing are not composed of salt and water, but the realm of numbers – complex numbers. This is no ordinary expedition, as you’re exploring the abstract and fascinating world of imaginary and complex numbers, mapping them onto planes, observing their behavior under different operations, tracing recursive patterns, and even spotting the elusive Mandelbrot Set. Buckle up, and let’s start the journey!

The Imaginary and the Complex

Imagine, pun intended, you encountered an unknown sea creature, described by the number [latex]4 + 5i[/latex]. Can you identify if this is a real number or a complex number?

Plotting the Course

As a navigator, you need to plot your coordinates on a map. If your current position is represented by the complex number [latex]-3 + 4i[/latex], can you plot this position on the complex plane?