Thanks for your additonal comment.
My initial question could have been answered with a yes or no but you answered it with a question. This required me to try to understand based on your question. I was quite willing to do that in order to enable my understanding the subject better.
In reading about this subject elsewhere, I am pretty sure mention was made that systems of numbers (maybe 'systems' is the wrong word) evolved to accomodate issues in mathematics which could not be resolved using previously existing knowledge. Negative numbers were one such development, imaginary numbers another. To understand your answer/question, then, I concluded you were speaking from this perspective, ie there are different systems.
If someone were to ask me now if both 2 and (-1 + i (3^.5) are equal to each other, I would say each is a cube root of 8, they are not equal to each other, and I will continue to attempt to learn why they are not equal to each other..