How did imaginary numbers come into existence? What was the first problem that required use of imaginary number?

Question

How did imaginary numbers come into existence? What was the first problem that required use of imaginary number?

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Answer 1

Several commenters have answered when our *understanding* of imaginary numbers were developed. However, the specific phrasing here – when did they come into *existence* – lets us touch on an interesting point in mathematics:

It is currently debated in the philosophy of mathematics if mathematical truths are invented or discovered. That is to say, it’s not clear to us if mathematics are a property of the universe, in which case it is discovered as a branch of science, or if they are a logical construct where mathematics are developed from philosophy ex nihilo.

By that first interpretation, for instance, we would expect that imaginary numbers came into existence with the Big Bang, and were left *undiscovered* until attempts to solve the cubic. While in the second, they didn’t exist until we thought about them.