Let us do something many companies fail to do - an impact analysis on the impact of having incomplete, ambiguous, or - otherwise sucky requirements. The requirements analysis efforts (something many companies fail to do) showed many incomplete, ambiguous, or - otherwise sucky requirements. The impact analysis reveals that major difficulties will be encountered during design, development, testing, deployment, and post-deployment support - if a product can be created to begin with, because of the shoddy requirements.
... and the two are mutually exclusive. One does not need to do an impact analysis as related to requirement analyses. or - for that matter anything. Unfortunately in this industry too little of both are done.
As per my understanding, Requirements analysis is something that is done for the purpose of meeting the user needs whereas impact analysis is something which helps in finding the risks/impact a particular requirement may have on the system because of the non-feasibility of the requirement with in the given deadline or the effect of the requirement on the other business functionality or the business itself.
Requirements are synonym to "User's Needs". This means that a system is built to conform to those requirements (and thus fulfilling those needs), this usually is done in the early phases of the Software development process. So from the above definition, we can define Requirements Analysis as the "Validation of the needs specified by the User"
An already built system might often need to have additional functionalities (e.g Change Requests), These requests needs to be validated as well and their "Impact" on the system should be analyzed at all levels. The new requirements will almost always have some effect on the current behavior of the system, the process to Analyze these effect can be termed as "Impact Analysis"