To faze is "to disturb; discomfit; daunt", according to the Macquarie Dictionary. It's often used in expressions such as "I'm not fazed" to express a "no worries" attitude. That's fine, but don't write it as "I'm not phased". That conveys a "no brains" attitude.
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As always with homophones, I can understand how someone who has never seen this written down before might choose the wrong version. Phase is much more common, both as a noun and a verb. But that doesn't mean it's the version you want. It's yet another distinction you have to learn to write effectively. Accuracy matters.
Lifehacker's Mind Your Language column offers bossy advice on improving your writing.