Real-Life Applications of Complex or Imaginary Numbers

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Yes, it is possible to finish a quadratic with an imaginary number. If you've noticed, this is acceptable in higher levels of math but not in normal math or lower algebra. Where would this be used? Often, these type of problem solutions occur in engineering problems, physics problems, and most often, in space engineering and technology. Unless the student of math is on a course to take higher levels of math and work in the fields in which imaginary numbers become common, it is best to merely accept that those are ideals that seem to have worked for many years.

Without a formula, many common practices that we deal with in our every day life would not be understood. How could a carpenter build a specified item without knowing area or perimeter? How could a carpet-layer know how to cut a carpet for exact room size without a formula? How could pharmacists know how to mix medicine without formulas? Although sometimes exact numbers are not known, it is usually because of "rounding" to a certain amount of spaces. What you will find is that the more "exact" a computation has to be, the more accurate we must figure the variables.

http://www.math.toronto.edu/mathnet/answers/relevance.html

Okay, now we've seen that imaginary numbers exist. However, they exist in the context of a different number system, something different from the number systems we are used to. The "complex numbers" that make up this system are pairs of numbers; do they really deserve to be called "numbers" in their own right?
Well, remember that fractions are pairs of numbers also. They clearly deserve to be called numbers in their own right, since they can measure "how much" in some contexts (for instance, "I ate three quarters of a pie"). So, the principle of considering a pair of numbers (in this example, 3 and 4) as a number in its own right is well established.

The fact remains, though, that complex numbers have much less direct relevance to real-world ...