# Condition on Pointwise convergent sequnce on complex valued function to be uniform convergent

I Know that Pointwise convergence of continous sequnce of real valued function can be said to uniform converges BY Dini's Theorem By assuming Some condition like Monotonicity and compactness .
As there is no order in Complex number so monotonic condition can be removed.
That means Any point wise complex valued function is uniform convergent over compact set
Is this true?
How to prove this fact?

Or Is there any Condition Like Dini's theorem such that we can say pointwise convergece under that condition is uniform convergence complex ? Any Help will be appreciated

Consider the function $f_n(x) = i x^n$ defined on the compact domain $[0,1]$. $f_n$ converges pointwise to a function $f$ that is zero everywhere except at $1$, where it takes the value $i$ (i.e., $f$ is discontinuous).
Note that this does not really have much to do with complex numbers as you can replace $i$ with any constant of your choosing; I just wanted to give you a counterexample with nonzero complex part.