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Certain functions, when solving to find the zeros (value which makes the function equal zero), the only value which will work has an imaginary component. Note that a parabola (graph of a quadratic or 2nd order polynomial) can touch the x-axis at a single point, or 2 points or no points. If it does not touch or cross the x-axis, then the root (or zeros) of the function are complex with imaginary components.

Technically, all real numbers are a subset of complex numbers, so all numbers are complex - but this is not how we normally refer to them. We usually say that a number is real, or it is imaginary, or it is complex.

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Q: Where do you find complex numbers in algebra?
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