Angular2 with Firebase - Cannot read property 'database' of undefined

Question

I am using Ionic, Angular2, and Firebase in my application.

When the user registers I want to send data the my database and populate the user's profile.

Here is what I am doing:

app.module.ts:

import { AngularFireDatabaseModule } from 'angularfire2/database';
...
imports: [
  BrowserModule,
  IonicModule.forRoot(MyApp),
  AngularFireModule.initializeApp(FIREBASE_CONFIG),
  AngularFireAuthModule,
  AngularFireDatabaseModule, //<-- angular firebase database
  IonicStorageModule.forRoot()
],

login.ts:

import { AngularFireDatabase } from 'angularfire2/database';
...
export class LoginPage {
  user = {} as User;

  constructor(
    private afAuth: AngularFireAuth,
    private storage: Storage,
    private database: AngularFireDatabase, //database
    public navCtrl: NavController,
    public navParams: NavParams) {

  }

  //this code gets called when the user presses the register button
  async register(user: User) {
    try {
      const result = await this.afAuth.auth.createUserWithEmailAndPassword(user.email, user.password);
      this.afAuth.auth.currentUser.updateProfile({
        displayName: user.displayName
      }).then(function() {
        let currentUser = result;
        let userData = {
          email: currentUser.email,
          name: currentUser.displayName,
          uid: currentUser.uid,
          created: new Date(),
        }
        this.database.list('users').set(userData.uid, userData); //<-- This is where error occurs.
      }, function(error) {
        console.log(error)
      });
      console.log(result);
    } catch(e) {
      console.log(e);
    }
  }

}

Everything seems to work great apart from the database stuff. I can register a user and also login but when I try to send userData to my database I get the error:

ERROR TypeError: Cannot read property 'database' of undefined

Does anyone have any idea? I'm new to Angular2 so it might be a really simple fix!

Thank you.