Answer
$-ie^2$
Work Step by Step
$e^{2-i(\frac{\pi}{2})} = e^2e^{-i\frac{\pi}{2}}$
Applying Euler's equation to $cos(-\frac{\pi}{2}) + isin(-\frac{\pi}{2}))$
$cos(-\frac{\pi}{2}) = 0, isin(-\frac{\pi}{2}) = - i$
$-ie^2$
Elementary Differential Equations and Boundary Value Problems 9th Edition
by Boyce, William E.; DiPrima, Richard C.
Published by
Wiley
ISBN 10:
0-47038-334-8
ISBN 13:
978-0-47038-334-6
Chapter 3 - Second Order Linear Equations - 3.3 Complex Roots of the Characteristic Equation - Problems - Page 163: 4
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