map over list of functions

Question

I would like to convert a list of n complex equations to a list of 2n real ones. At the moment I am doing it like this:

eqs = {a + I b == 0, c + I d == 0}
Flatten[{ComplexExpand[Re[First[#]]] == 0 & /@ eqs,  
         ComplexExpand[Im[First[#]]] == 0 & /@ eqs}] 

I would like to know how I can write this more compactly, since I'm basically using the same command twice, with the only difference being changing the function Re -> Im. Perhaps I can use a pure function to map over a list of these 2 functions?

Thanks!

Answer 1

I would probably do something like this:

eqs = {a + I b == 0, c + I d == 0};

Join @@ Thread /@ ComplexExpand @ Map[{Re@#, Im@#} &, eqs, {2}]

{a == 0, b == 0, c == 0, d == 0}

Or shorter:

Join @@ ComplexExpand[Map[#, eqs, {2}] & /@ {Re, Im}]

{a == 0, c == 0, b == 0, d == 0}

The order is slightly different, if it matters.