Numbers less than Zero

The complex numbers have a real part and an imaginary part. This imaginary part have been a confusion for quite some time to me. I thought, if it does not exist then why we need that? But the point is, these numbers exist in nature but we do not know the calculable answer for them with known mathematical rules. For example the square root of negative numbers is not equal to a real number so we imagine that as i for calculations sake. Therefore, by definition an imaginary unit i is equal to square root of -1 (i =sqrt(-1)). An Italian mathematician Gerolamo Cardano conceived the concept of complex numbers around 1545. He was the first mathematician to use numbers less than zero in a systematic manner.  Since then rules and algorithms for different operations on complex numbers have been developed by a number of mathematicians.