$x(t) =e^{-t} (\cos t+i\sin t)$ determine $x(t)$ is periodic or nonperiodic and the period if its periodic
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and what have you done? Unrelated, are you an engineer? – Zelos Malum Dec 11 '15 at 14:16
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1Of course he is. Mathematicians write $i$ not $j$ in their complex numbers. – GEdgar Dec 11 '15 at 14:17
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That is what tipped me off – Zelos Malum Dec 11 '15 at 14:17
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1Welcome to the site. Remember to include your own thoughts on a problem and tell us where you are stuck. – Mankind Dec 11 '15 at 14:21
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$x(t)\to 0$ thus not periodic – Piquito Dec 11 '15 at 14:42
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It can't be periodic, since the length of the function is strictly decreasing.
Indeed, if $t_1<t_2$, then
$$|x(t_1)| = |e^{-t_1}(\cos(t_1)+i\sin(t_1))| = |e^{-t_1}| > |e^{-t_2}| = |e^{-t_2}(\cos(t_1)+i\sin(t_1))|=|x(t_2)|,$$
where I have used that $(\cos(t)+i\sin(t))$ is always a point on the unit circle, and hence has length $1$.
Mankind
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