[eli5] Why is imaginary number root -1? Why not root -n, since no number times each other would result in negative number?

Question

[eli5] Why is imaginary number root -1? Why not root -n, since no number times each other would result in negative number?

In: Mathematics

Answer 1

All numbers that can be written as √(-n) where n is a real number are imaginary.

Only √(-1) is the imaginary *unit.*

Think of it like “north” or “°C” or “meter.” It’s not that √(-1) is special because it’s somehow any more or less like any other number that is the square root of a negative number. Instead, it’s that it is the *simplest* such number, just as 1°C is the simplest *unit* of Celsius temperature or 1m is the simplest *unit* of metric distance.