Proove e^(z+2{pi}nj) is a periodic function - only for n being an integer - have i gone wrong
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Proove e^(z+2{pi}nj) is a periodic function - only for n being an integer - have i gone wrong

[From: ] [author: ] [Date: 11-05-08] [Hit: ]
.whats it done exactly, for n being an integer i agree as sin(0) = 0 and cos(0) = 1..........
so its a simple thing my book says where
we'll use:
t for theta
p for pi
z for a general complex number
j = (-1)^0.5

e^(z+2npj) = e^z

so lets look at this:
e^(z+2npj) = e^z * e^(2npj)
= e^z * (cos(2pn)+j sin(2pn)) which i agree with
the book then says
= e^z * 1
this is where it loses me....what's it done exactly, for n being an integer i agree as sin(0) = 0 and cos(0) = 1....
thanks

-
cos(2pi n) = 1, if n is an integer.
sin (2pi n) = 0, if n is an integer.
1
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