

Well, even 18th century's mathematicians were puzzled and didn't know what to do with it.

They were the top 0.001% high IQ people.
In Europe, dominated by Greek heritage (Greeks were very good at geometry), and to most of the mathematicians the square root -1 did not make any sense.
Let's think about area. Area of 9 square has 3x3 sides. So, how the area could be -1?
They did not want to deal with things that's not real.

Imaginary Number - History
Prelude
Math is everywhere!
It is mostly about numbers: weight, size, money, etc.
Let's think about the size (scale). The smallest scale for most of us is probably mm and the largest scale in our daily life might be less than 100,000km.
Actually, the smallest scale known to us is Planck length (lP) which is equal to 1.616199(97)x10−35 meters, and the biggest scale is observable universe which is 28.5 Gparsecs (93 billion light-years, 8.8×1026 metres or 5.5×1023 miles).
In our everyday life, there are quite a few intersting numbers such as Fibonacci and weird ones such as imaginary numbers.
Well, it's not just numbers. There are several equations such as Newton's 1st law which affects all objects on earth, F=ma and Schrodinger equation that's being used in quantum physics:

This site will try to explain or describe mathematics the most easiest ways possible: pictures, drawings, videos, or simple formulas.
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"Do not worry too much about your difficulties in mathematics, I can assure you that mine are still greater." - Albert Einstein.