Is the following sentence a complex sentence?

As a result of showing my gregarious personaity, I have many friends.

No, it's not complex. Before the comma, there needs to be a clause, not a phrase.

Did you find my correction below??

Let me know how you decide to correct this.

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how about...

Now that I show my gregarious personality, I have many friends.

Excellent! Now both are clauses -- do you see why the first one did not have two clauses?

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Yes, I think. Is it because As a result.. isn't a subordinator?

Subordinating conjunctions are just one type of "signal" word for the beginning of subordinate clauses. Here are a few:

as
if
as if
as though
although
when
after
while

Scroll down for Coordinating Conjunctions: http://grammar.ccc.commnet.edu/grammar/conjunctions.htm

Relative pronouns can also introduce subordinate clauses: http://grammar.ccc.commnet.edu/grammar/pronouns1.htm#relative

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Thank you so much.

=) I think I actually understand...

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You're welcome! I'm glad I could help you understand. If you have any more questions, feel free to ask! 😊