### 22 Answers

- Jeffrey KLv 61 month ago
Do fractions exist? Do negative numbers exist? Do irrational numbers exist? It depends on what mathematical system you are using and what physical problem you are working on. If you are counting people, fractions make no sense.

Math starts with the counting numbers and extensions can be made to accommodate the situation. In terms of Abstract Algebra, imaginary numbers along with real numbers form a complete ring and field. Every operation done on a complex number yields another complex number.

Extensions can still be made to complex numbers. For example, quaternion numbers, octernion numbers, surreal numbers, Cayley numbers, transfinite numbers, .....All these abstract types of numbers have their uses.

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- Ian HLv 71 month ago
Mathematicians used to be nervous about negative numbers. Negatives extend the concept of number and their usefulness is widely accepted. But ask yourself does the concept minus 6 exist ? You cannot see it, or hold it, and young children might complain that it is difficult to give someone minus 6 apples; but you can think about it in an abstract way, and like overdrafts they have conceptual reality.

In a similar way, complex numbers extend the concept of numbers even further and they allow us to solve problems related to very real situations. It is unfortunate that the square roots of negatives got the name imaginaries

Without yet dwelling on what it ’means’, the square root of minus one can be said to exist inasmuch as we can conceive of it; and we may certainly use it.

The squared and fourth powers of i have real interpretations. Also, with the benefit of hindsight, complex numbers have a multiplicity of uses. These observations encourage us to treat i as an entity which should not be ignored.

- fcas80Lv 71 month ago
The square root of negative one is a perfectly fine number. Why would anyone think otherwise>

- PuzzlingLv 71 month ago
In the words of Descartes, "I think, therefore I am".

I don't think I'm imagining that quote.