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## Homework Statement

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)=y

_{re}(t) + iy

_{im}(t), where y

_{re}(t) and y

_{im}(t) are real valued, then both y

_{re}(t) and y

_{im}(t) are solutions of the second-order equation.

## Homework Equations

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 :)