Below is the signal :
$y[n] = j ^ n$
Someone told me that the period is 4 ,but he didn't explain me why. Can anyone help me ?
2026-03-25 23:52:26.1774482746
What is the period of this signal?
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I presume that "j" here is the "imaginary unit", that I would call "i", the principal square root of -1 in the complex number system. By definition then $j^2= -1$. Then $j^3= j(j^2)= j(-1)= -j$ and $j^4= (j^2)(j^2)= (-1)(-1)= 1$. If we continue the same way we get $j^5= j$, $j^6= -1$, $j^7= -j$, $j^8= 1$, etc. Every power of j that is a multiple of 4 gets us back to 1 so the sequence of powers repeats every 4 places. It is in that sense that multiplication by j is "periodic with period 4".