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Good Math by Mark C. Chu-Carroll

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What i Means

But what do complex numbers mean in the real world? Do they really represent actual phenomena, or are they just a mathematical abstraction?

The answer is that they’re very real, as any scientist or engineer will tell you. There’s one standard example that everyone uses because it’s so perfect: Take the electrical outlet that powers your lights, your computer. It provides an alternating current. What does that mean?

Well, the voltage—which (to oversimplify) can be viewed as the amount of force pushing the current— is complex. In fact, if your outlet supplies a voltage of 110 volts AC at 60 hz (the standard in the US), that means the voltage is a number of magnitude 110. In Figure 7, Alternating current in the complex plane: ...

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