I stumbled upon the following exercise:
Find complex roots of a polynomial $x^2 - 5x + 7 - i$. The problem I have with this is not in the fact that I cannot solve it (I actually did), but I am searching for a more efficient or "smart" way of doing this.
The way I approached this problem was by writing x as a complex number ($x = a + bi$) and then substituted $x$ in the equation $x^2 - 5x + 7 - i = 0$. Then, after some rearranging I got two equations and solved the system for a and b. My result was correct, however, I am not satisfied because my method is rather tedious and I would like to hear from you, how to make this easier if possible.
Note: I have tried solving this as a quadratic equation the usual way, however, I stumbled upon $\sqrt{4i - 3}$ in the solution and I am not sure how to simplify this.