Show that the only singularities of tanz are simple poles at (2n + 1)π/2[15] with n ∈Z.
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The meaning of singularity is that the function is not defined at that point.
Tan z is not defined at when tangent of an angle is 90°.
→tan z=tan 90°
→As we know general solution of tan A=tan B is A=nπ+ B
→So , solution of⇒ tan z=tan 90° is z=nπ+π/2 where n∈Z
So, tan z is not defined at π(n+1/2)=π/2(2 n+ 1) where n∈Z
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