The primary purpose of a module in AngularJS is encapsulating components. Modules help organize and structure an AngularJS application by grouping related components, services, and directives together. This encapsulation enhances modularity, maintainability, and code reusability in AngularJS projects. Understanding the role of modules is fundamental for creating well-organized and scalable AngularJS applications.

AngularJS expressions can be leveraged in a complex application for dynamic content rendering through various techniques. Using ng-repeat allows developers to iterate over a collection and generate dynamic content on the fly. Embedding expressions in custom directives enables the creation of reusable components with dynamic behavior. Additionally, utilizing expressions in routing configurations allows for dynamic page rendering based on user interactions. A comprehensive understanding of these approaches is essential for building scalable and dynamic AngularJS applications.

The ng-click directive in AngularJS is used to execute a function in the controller when a specified event (such as a button click) occurs. This directive binds the specified expression to the click event, allowing developers to define custom behaviors when the associated element is clicked. Understanding how to use ng-click is essential for handling user interactions in AngularJS applications.

The ng-model directive in AngularJS creates a two-way binding between the model and the view. This means that changes in the model automatically update the view, and vice versa. It is commonly used in forms to handle user input and keep the model and view in sync. Understanding ng-model is crucial for building interactive and responsive user interfaces in AngularJS applications.

To avoid polluting the global scope, controllers should be encapsulated within a module. Modules in AngularJS act as containers for different components of an application, providing a way to organize and structure the code. Encapsulating controllers within modules helps in managing dependencies, improving code maintainability, and preventing naming conflicts in large applications.

Deep watching an object in AngularJS for data binding in a controller can have implications on performance. Deep watching involves monitoring changes at nested levels within an object, and if not used judiciously, it can lead to performance issues by triggering frequent digest cycles. Developers need to be cautious when employing deep watches to avoid unnecessary overhead in complex applications.

The role of $injector in AngularJS's dependency injection mechanism is to resolve and inject dependencies into AngularJS components. It is responsible for managing the dependency injection process, ensuring that the required services or objects are available when needed. Understanding the $injector is essential for implementing and customizing dependency injection in AngularJS applications.

In AngularJS, the ng-component directive is used for creating reusable components that manage their own view. Components encapsulate both the template (view) and the logic (controller) associated with a specific part of the user interface. Using components enhances code organization, reusability, and maintainability in AngularJS applications.

To effectively isolate a directive's $scope, the scope property is used in the directive's definition. By setting the scope property to true or an object, you can create an isolated scope for the directive. This helps in encapsulating the directive's behavior and preventing unintended interactions with parent scopes. Understanding scope isolation is essential for building modular and reusable directives in AngularJS applications.

In AngularJS, Observables are used to deal with multiple HTTP requests to an external API asynchronously. Observables represent a sequence of values over time and provide powerful features for handling asynchronous operations, such as HTTP requests. Observables support operators that enable developers to transform, filter, and combine data streams, making them a flexible and efficient choice for managing asynchronous tasks in AngularJS applications.