ðɪs pɹəvˈaɪdz ˈɪnsaɪt tə ðə fluːˈɪdᵻɾi ʌv kˈɑːmplɛks fˈʌŋkʃənz ænd ʃˈoʊz nˈætʃɚɹəl dʒˌiːoʊmˈɛtɹɪk ɛkstˈɛnʃənz ʌv ɹˈiːəl fˈʌŋkʃənz.
This provides insight to the fluidity of complex functions and shows natural geometric extensions of real functions.