The golden ratio is a number often encountered when taking the ratios of distances in geometric figures.
Application: The golden ratio is often used in financial technical analysis to attempt to determine when a market will continue its path or reverse.
It's also observed very frequently in nature, especially in the way that some naturally occurring spirals expand outward.
Source: Forexoma
"i" equals the square root of -1, which means that i squared is equal to -1.
Application: Negative numbers don't have square roots. Math had advanced to the point where saying "there is no square root of negative numbers" was holding back a lot of progress.
Solutions of some polynomials have both real solutions that we could use in real life as well as solutions that involved the square root of a negative number, which can be discarded.
Source: Wolfram
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