Question

I have the auxiliary equation \[r^2-4r+13=0\]
The roots are imaginary, but I forgot how to determine them.

Answer 1

complete the square is easiest here
\[x^2-4x=-13\]
\[(x-2)^2=-13+4=-9\]
\[x-2=\pm\sqrt{-9}=\pm3i\]
\[x=2\pm3i\]

Answer 2

makes sense. Thank you!

Answer 3

yw