A Visual Intro to Complex Numbers
This article provides a visual and algebraic introduction to complex numbers, demonstrating how certain quadratic equations cannot be solved using only real numbers. It walks through an example, illustrating the necessity of complex numbers when encountering the square root of a negative number in algebraic solutions.
Why it matters
Understanding complex numbers is fundamental in various scientific and engineering fields, including electrical engineering, quantum mechanics, and signal processing, enabling solutions to problems intractable with real numbers alone.
Nick M Oct 01, 2026 14 4 1 Share We’ll start off our journey by attempting to solve the systems of equations provided below:
At first this resembles an ordinary system of two equations – but if we just spend a small amount of time attempting to plug in regular whole / real numbers, you’ll be able to see a bit of a dilemma. Let’s try plugging in 3 for both x and y:
Let’s try plugging in 4 and 2 now to see if this gets us any closer:
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