Nice article, but I always found the â€śbestâ€ť way to understand math is by its history, especially how mathematical idea came into being. No one actually wanted to solve

x^2 = -9

, nor want to â€śtake the square root of nothingâ€ť. But in the 1500s, Bombelli wanted to use one of Cardanoâ€™s formula to solve

x^3 = 15x + 4

, and get

x = cuberoot(2 + sqrt(-121)) + cuberoot(2 â€“ sqrt(â€“121))

After figuring that

cuberoot(2 + sqrt(â€“121)) = 2 + sqrt(â€“1)

cuberoot(2 - sqrt(â€“121)) = 2 - sqrt(â€“1)

, he found the real solution

x = 4

The idea was that this number sqrt(-1) was actually useful!

And yeah, everyone should also see the (simple) proof of Eulerâ€™s formula. It is Eulerâ€™s formula that links trigonometry to arithmetic (and allows for a geometric interpretation of complex numbers as a result).