I'm surprised to find a huge mistake at the very beginning of this article. Complex numbers were introduced by italian algebrists to make sense of their method to solve third degree equations who had real solutions but the formulas made use of square roots of negative real numbers. They were very reluctangly introduced (hence the terminology imaginary numbers) because at the end the result was a real numberIt is true that once you have real numbers they can appear as solution of quadratic equations but that is not the reason they were introduced.