# Simplifing equation with complex coefficients

I'm trying to simplify an expression with complex coefficients. It should be very straightforward, but for some reason, I cannot get the correct answer. Please, see the code below:

Simplify[\[Gamma]0[0] == Re[(0.5852908990577314 + 1.831942535298071 I)*\[Gamma]0[
1] + (0.25530515981369933 + 0.6158107565352037 I)*\[Gamma]0[
3]], {Element[\[Gamma]0[1], Reals],
Element[\[Gamma]0[3], Reals]}]


It should return

0.585291\[Gamma]0[1] + 0.255305\[Gamma]0[3] == \[Gamma]0[0]


But returns

Re[(0.585291 + 1.83194 I) \[Gamma]0[
1] + (0.255305 + 0.615811 I) \[Gamma]0[3]] == \[Gamma]0[0]


Can't really find my error. Thank you for your help!

Use ComplexExpand

\$Version

(* "14.1.0 for Mac OS X ARM (64-bit) (July 16, 2024)" *)

Clear["Global*"]

γ0[0] ==
Re[(0.5852908990577314 + 1.831942535298071 I)*γ0[1] +
(0.25530515981369933 + 0.6158107565352037 I)*γ0[3]] //
ComplexExpand

(* γ0[0] == 0. + 0.585291 γ0[1] + 0.255305 γ0[3] *)

% // Rationalize

(* γ0[0] == 0.585291 γ0[1] + 0.255305 γ0[3] *)

• Thank you, that worked perfectly. Commented Aug 12 at 21:26
eqn = γ0[0] == (0.5852908990577314 + 1.831942535298071  I)*γ0[1] +
(0.25530515981369933 + 0.6158107565352037  I)*γ0[3];


Using ReplaceAll:

Reverse[eqn /. x_Complex :> Re[x]]


0.585291 γ0[1] + 0.255305 γ0[3] == γ0[0]`

• Thank you, that worked perfectly. Commented Aug 12 at 21:26