# What does 1 red 1 unit mean

## What is 1 / i? - The mathematical expression simply explained

"1 / i" is a strange expression and you can hardly believe that it should have anything to do with mathematics. "I" is the so-called imaginary unit that was "invented" by mathematicians in order to be able to extract the root from negative numbers.

### What you need:

- Basic knowledge of "roots"

### Root of -1 - mathematicians define the "i"

- Mathematics has made expansions in the entire range of numbers if a type of calculation required it. For example, negative numbers were "invented" in order to post debit amounts or to always be able to carry out subtractions. Fractions also owe their existence to the desire to be able to divide without remainder.
- However, it is very unsatisfactory not to be able to take roots from negative numbers. So you simply defined a new type of number, namely the complex numbers with which this succeeds.
- The complex numbers are based on the imaginary unit "i", which was defined as follows: i = root (-1), consequently i² = -1.
- Roots from negative numbers can thus be solved, because it is, for example, the root (-4) = 2i.

### But what does 1 / i mean?

- Of course, you can calculate with imaginary and complex numbers, that is, those with real and imaginary parts such as 2-3i, almost as well as with real (the "correct") numbers.
- So you can add and subtract, but also multiply and even divide.
- 1 / i is initially nothing other than that the number "1" is divided by "i" or the reciprocal of "i".
- With a little skill, this division or this reciprocal value can be converted into an expression that is easier to understand and with which one can calculate better.
- The trick is to expand the fraction with "i", that is, to multiply it by i / i (so that the value doesn't change). The following applies: 1 / i = 1 / i
_{*}i / i = i / -1 = -i (because i² = -1, see above).

Bottom line: The complicated looking expression 1 / i is nothing more than -i.

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