Made by Finian Knepper

Imaginary Number i

5 Facts About i

1. The √-1 was first described by Rafael Bombelli in 1579, but instead of i, he called it "pi´u di meno."

2. Leonard Euler was the first person to represent √-1 as i, in 1777.

3. i's full name is "Iota".

While we call it i, that's actually a nickname. The full name of i is "Iota."

4. i to the i'th power is a real number.

Strangely, i^i power is a real, countable number: Approximately 0.20788. This is found through the equation:

i = ei(π/2+2kπ)

e is a constant that = approximately 2.71828183

therefore i^i=(ei(π/2+2kπ))i = e−π/2−2kπ

k is just a variable, it can be anything.

If k=0, you get 0.207879576350761908.

5. i is commonly used in Electrical Engineering to calculate the relationship between an electrical current and voltage, and the Waveform of a current.

However, they use j to represent √-1, because in electrical engineering, i is already used to represent the strength of electrical current.

Sources:

https://www.papertrell.com/apps/preview/The-Handy-Math-Answer-Book/Handy%20Answer%20book/Who-first-came-up-with-the-idea-of-imaginary-numbers/001137022/content/SC/52caff7082fad14abfa5c2e0_default.html#:~:text=Some%20historians%20give%20credit%20to,Magna%20(The%20Great%20Art)

https://fiveable.me/key-terms/electrical-circuits-systems-ii/j-operator

https://math.hmc.edu/funfacts/i-to-the-i-is-a-real-number/

https://math.stackexchange.com/questions/546080/what-does-ii-equal-and-why

https://www.math.uri.edu/~merino/spring06/mth562/ShortHistoryComplexNumbers2006.pdf