Suppose y(t) is a complex-valued solution of y'' +py' + qy=0 where p and q are real numbers. Show that if y(t)=yre(t) + iyim(t), where yre(t) and yim(t) are real valued, then both yre(t) and yim(t) are solutions of the second-order equation.
We can use the idea that a complex numbers is zero as long as it's real and imaginary parts are equal to zero.
The Attempt at a Solution
I do not have an attempt at this solution. I do not know where to begin.
thanks for your help :)