Chapter 8.5, Problem 19P

Solve the algebraic equation $D^2+(1+2i)D+i-1=0$

(note the complex coefficients) and observe that the roots are complex but not complex conjugates. Show that the method of solution of (5.6) (case of unequal roots) is correct here, and so find the general solution of $y^{\prime \prime }+(1+2i)y^{\prime }+(i-1)y=0$.