Ambiguous and incomplete are two distinct concepts. You can check the definitions in any reputable dictionary, but here is some illumination:
Statements can be ambiguous without being incomplete:
“Welcome, O life! I go to encounter for the millionth time the reality of experience and to forge in the smithy of my soul the uncreated conscience of my race.” —James Joyce, A Portrait of the Artist as a Young Man
Here the ambiguity lies in the verb to forge, which splits along two lines: forging as a constructive process ("a blacksmith forges weapons") and a duplicitous one ("a thief may forge your signature on a check", "this painting is a forgery"). This sort of ironic wordplay was bread and butter to Joyce. But the statement in the novel is certainly complete.
Statements can be incomplete without being ambiguous:
A: Can I borrow a dollar?
B: I don't have any money.
B may have money, just none to lend to A. The statement is incomplete, but there is no ambiguity, since for the purposes of the conversation there is no money and a further explanation is not required.
A statement may be ambiguous because it is incomplete:
I like the way you move [my furniture].
Leaving out the furniture leaves the statement open to multiple interpretations.