Cannot apply FindMaximum/FindMinimum on a list of function invoking styled symbols

Questions
1

Hi. there
We can use Re[unevaluated_symbol] as a symbol in Minimize. but in FindMinimum.
How can we resolve this?

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2

Here is a way:

FindMinimum[Re[a]^2 + Re[b]^2, {a, b}]