Algebraning fundamental teoremasi shuni ko'rsatadiki, har bir murakkab koeffitsiyentli o'zgarmas ko'phadning kamida bitta murakkab ildizi bor. Dastlabki dalil: Biz bu teoremani ziddiyat orqali isbotlaymiz. Faraz qiling, murakkab koeffitsiyentli o'zgarmas ko'phad P(z) mavjud. Agar murakkab ildizlari bo'lmagan bo'lsa. P(z) o'zgarmas bo'lsa, u eng yuqori darajali hadga ega, deylik azn. Biz a nolga teng emas deb taxmin qilishimiz mumkin, aks holda P(z) o'zgarmas ko'phad bo'ladi. Funksiyani f ((z) = 1/P ((z) deb ko'ring. Ushbu funksiya P ((z) ning ildizlaridan tashqari barcha z uchun yaxshi belgilangan. P
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