It sounds like you might be trying to run the command from the MySQL shell, instead of the Windows command line. If your prompt looks like this:
mysql>
then you're in the MySQL shell. That would explain why you're getting a syntax error. It's expecting SQL statements.
mysqldump is a separate program, so you just need to run it from the Windows command line. Your prompt should be something like this, depending on where MySQL is installed:
C:\mysql\bin>
Hope that works for you.
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