I have been reading A Long Way From Euclid a book by Constance Reid. In the chapter on complex numbers she gives an equation, and the solutions to the equation, but does not show how the solutions are arrived at. I am stumped, and (finally) realize I need help. Just as important as knowing how to solve this equation where i equals "1" i, I would like to know how to solve it if the i equals 2i, 3i, 4i. . .ni, where n is any real number. Can the equation be solved algebraically by converting the x and the i into a + bi form? Or, does DeMoivre's theorem for finding complex roots have to be used? Both? Or, somthing else?
The equation is
The solutions that Reid gives are --