Relate the well-known power series from Calculus I, e* = E and the п! n=0 power series for sin x and cos x to show that elx = cos x + i sin x, for all x E R. Then for a + ib e C, explain the formula ea+ib e (cos b +i sin b).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Relate the well-known power series from Calculus I, e*
En=0
and the
n!
power series for sin x and cos x to show that elx
= cos x + i sin x, for all x E R.
Then for a + ib E C, explain the formula ea+ib
= ea (cos b + i sin b).
Transcribed Image Text:Relate the well-known power series from Calculus I, e* En=0 and the n! power series for sin x and cos x to show that elx = cos x + i sin x, for all x E R. Then for a + ib E C, explain the formula ea+ib = ea (cos b + i sin b).
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