Find the derivatives F'(t) and F''(t) for each of the following complex-valued functions of the real variable t. (a) F(t)=e^{(1−i)t} (b) F(t)=e^{3 i t

remolatg 2021-06-23 Answered

Find the derivatives F'(t) and F''(t) for each of the following complex-valued functions of the real variable t.
(a)F(t)=e(1i)t
(b)F(t)=e3it
(c) F(t)=e(2+3i)t

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comentezq
Answered 2021-06-24 Author has 106 answers

(a)Let F(t)=e(1i)t. Then F(t)=(1i)e(1i)t and F(t)=(1i)2e(1i)t=2ie(1i)t.
(b) Let F(t)=e3it. Then F(t)=3ie3it and F(t)=(3i)2e3it=9e3it.
(c) Let F(t)=e(2+3I)t. Then F(t)=(2+3i)e(2+3i)t and F(t)=(2+3i)2e(2+3i)t=(5+12i)e(2+3i)t.

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