I am trying to do the following :
How do I obtain an expression for $\epsilon$
Format[σ0] = Subscript["σ", 0]; Format[ϵ0] = Subscript["ϵ", 0]; σ = σ0/(1 - I ω τ); ϵ = ϵ0 (1 + I σ/(ω ϵ0)); Simplify@ϵ
Simply, subscripts don't work like that in Mathematica. When you define $\epsilon=\epsilon_\theta$, the $\epsilon$ on the right hand side is then substituted with the definition, because $\epsilon_\theta$ is not actually treated as its own variable.
σ = σθ (1 - I ω τ); ϵ = ϵθ (1 + I σ/(ω ϵθ)); Simplify[ϵ]
ϵθ + σθ (τ + I/ω)
Please also note that
Simplify ϵ is literally interpreted as
ϵ, and will not result in any simplification. The square brackets are necessary for
Simplify to have any effect.
Please also note that as written in your screenshot, the imaginary unit
I will not be evaluated, as it is part of a variable name. To multiply
I by something, make sure there is a
* (asterisk) between them.