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I am trying to do the following :

enter image description here

How do I obtain an expression for $\epsilon$

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  • $\begingroup$ Why don't you trivially cut-and-paste the definition of σ from the first equation into the second and be done? Your syntax is all wrong too: Simplify[ ]. And there is no reason your Simplify call "knows" the first definition you've given. $\endgroup$ Commented Feb 6, 2018 at 23:20
  • $\begingroup$ Even after doing that I am not getting a simplified expression. $\endgroup$ Commented Feb 6, 2018 at 23:24
  • $\begingroup$ You could consider one of the options presented in this answer $\endgroup$
    – Carl Woll
    Commented Feb 6, 2018 at 23:47

2 Answers 2

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Using Format

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

enter image description here

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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 Simplify times 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 (space) or * (asterisk) between them.

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  • $\begingroup$ But I want the Sigma from equation 1 to be substituted into equation 2. $\endgroup$ Commented Feb 6, 2018 at 23:27
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    $\begingroup$ Then put a space between the imaginary unit and the sigma, otherwise it's one variable. Will edit that in momentarily. $\endgroup$
    – eyorble
    Commented Feb 6, 2018 at 23:29

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