The fastest way is to log in to the Azure portal and select your web application from the resources menu. Once you open the blade for your web application, there are two types of IP addresses. Inbox and outbox. For the outbound IP address, click properties on the resource menu. This will display a list of all possible outgoing IP addresses.

For the incoming IP address, click "User Domains" in the properties menu, and the external IP address will appear there.

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