People thought negative numbers were weird until the 1800s or so, they arose in much the same way as a way to solve algebraic equations (or even just to balance

People thought negative numbers were weird until the 1800s or so, they arose in much the same way as a way to solve algebraic equations (or even just to balance the books, literally). Complex numbers were always going to show up just so we could diagonalise matrices, which is an important part of solving (linear) differential equations.