Imagine – imaginary numbers! What could this mean? Something made up by mathematicians with way too much time on their hands? What are these folks going to think of next? Algebra teachers have long known that equations of the form x2 = 16 have two solutions, +4 and -4. But when asked to solve the equation x2 = -16, most people say “there is no such animal” that can be squared and equal a negative number.
However, we can now find the answer to this, and other questions, and see this answer with great understanding and visualization by visiting the website of Kalid Azad. He has created a website, BetterExplained, with the byline “Learn Right, Not Rote“. His goal is to help people understand mathematics with incredibly lucid explanations. In the case of imaginary numbers, he focuses on relationships, not mechanical formulas, presents complex numbers as an upgrade to our number system, just like zero, decimals and negatives were, and uses visual diagrams, not just text, to understand the idea. His secret weapon is learning by analogy. He approaches imaginary numbers by observing its ancestor, the negatives.
Now Algebra 1 teachers can explore imaginary and complex numbers with their students with understanding and appreciation. Enjoy Kalid’s website and let me know what you think.
– Mr. L