Find all the complex roots of cosh z=1?

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Can't get started on this one. Any help would be greatly appreciated. Many thanks!

2007-10-07 05:50:26 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

e^z+e^-z = 2
put e^z= t
t+1/t= 2 so t^2 -2t+1= 0 so t = 1
e^z=1 = 1<2kpi
so z = i* 2kpi (k any integer)

2007-10-07 06:00:43 · answer #1 · answered by santmann2002 7 · 0⤊ 0⤋

cosh(z) = cos(i * z) = 1
z = 2*pi*i*k, where k=all integers

2007-10-07 13:00:32 · answer #2 · answered by MooseBoys 6 · 0⤊ 0⤋