How to synchronize DOM changes with model in AngularJS test

I am trying to simulate user actions and test AngularJS controller reaction on them.

describe('Testing a controller component', function () {
    beforeEach(inject(function ($compile, $rootScope, $httpBackend, $templateCache) {
        scope = $rootScope.$new();
        element = angular.element('<sign-up></sign-up>');
        element = $compile(element)(scope);
        scope.$digest();
        controller = element.controller('signUp');
        scope.$apply();
    }));

    it('should render template', function () {
        element.find('input').val('123');
        scope.$digest();
        expect(controller.firstName).toBe('123');
    });
});

The test fails due the model field is not updated.

Expected undefined to be '123'.
        at UserContext.<anonymous> (tests/calculator.controller.test.js:54:42)

I know it's against the AngualrJs approach, but I wan't use it for testing.