How Does Re[s]>0 Relate to Laplace Sine Transform Conditions?

[back2square1]

L[sin(at)]=\frac{a}{s^{2}+a^{2}}, Re<s>&gt;0</s>

L[e^{kt}]=\frac{1}{s-k}, s&gt;k
L[e^{-kt}]=\frac{1}{s+k}, s&lt;-k

L[sin(at)]=\frac{1}{2i}L[e^{iat}-e^{-iat}]
=\frac{1}{2i}L[e^{iat}]-L[e^{-iat}]
Using the above relations
=\frac{1}{2i}[\frac{1}{s-ia}-\frac{1}{s+ia}], s&gt;ia, s&lt;-ia

The problem is that I don't understand, how s>ia and s<-ia could imply that Real part of s>0?

 

[lurflurf]

Complex numbers are not ordered,
s>ia and s<-ia
does not make sense.
Real part of s>0
Is needed to assure the existence of the integral.