Chapter 3 - Second Order Linear Equations - 3.3 Complex Roots of the Characteristic Equation - Problems - Page 163: 2

$e^2(cos(3) - isin(3))$

$exp(2-3i) = e^{2-3i} = e^2e^{-3i}$ Applying Euler's equation to $e^{-3i}$ yields $cos(-3) - isin(-3)$ Cosine is an even function, so $cos(-3) = cos(3)$ Sine is an odd function, so $isin(-3) = -isin(3)$ $e^2(cos(3) -isin(3))$