--- title: Addition, Subtraction & Multiplication - Basic Operations description: Addition, subtraction, multiplication of complex numbers in a+bi form. The rules, worked step by step. url: https://astra-ai.co/videos/complex-numbers/addition-subtraction-multiplication/ locale: en type: video-chapter keywords: - addition, subtraction, multiplication - complex number operations - a plus bi - imaginary unit published: 2026-10-01T09:51:40.856Z updated: 2026-10-04T21:58:55.646Z alternates: bg: https://astra-ai.co/bg/videos/kompleksni-chisla/sabirane-izvazhdane-umnozhenie/ br: https://astra-ai.co/br/videos/numeros-complexos/capitulo-matematica-028/ cs: https://astra-ai.co/cs/videos/komplexni-cisla/scitani-odcitani-nasobeni/ da: https://astra-ai.co/da/videos/komplekse-tal/addition-subtraktion-og-multiplikation/ de: https://astra-ai.co/de/videos/komplexe-zahlen/addition-subtraktion-multiplikation/ el: https://astra-ai.co/el/videos/migadikoi-arithmoi/prosthesi-afairesi-kai-pollaplasiasmos/ en: https://astra-ai.co/videos/complex-numbers/addition-subtraction-multiplication/ en-IN: https://astra-ai.co/en-IN/videos/complex-numbers/chapter-ca42f548/ en-PH: https://astra-ai.co/en-PH/videos/complex-numbers/chapter-ca42f548/ es: https://astra-ai.co/es/videos/numeros-complejos/suma-resta-y-multiplicacion/ es-AR: https://astra-ai.co/es-AR/videos/numeros-complejos/capitulo-22/ es-CL: https://astra-ai.co/es-CL/videos/numeros-complejos/capitulo-22/ es-PE: https://astra-ai.co/es-PE/videos/numeros-complejos/capitulo-video-ca42f548/ et: https://astra-ai.co/et/videos/kompleksarvud/liitmine-lahutamine-ja-korrutamine/ fi: https://astra-ai.co/fi/videos/kompleksiluvut/yhteenlasku-vahennyslasku-ja-kertolasku/ fr: https://astra-ai.co/fr/videos/nombres-complexes/addition-soustraction-multiplication/ hr: https://astra-ai.co/hr/videos/kompleksni-brojevi/zbrajanje-oduzimanje-mnozenje/ hu: https://astra-ai.co/hu/videos/komplex-szamok/osszeadas-kivonas-es-szorzas/ id: https://astra-ai.co/id/videos/bilangan-kompleks/penjumlahan-pengurangan-dan-perkalian/ it: https://astra-ai.co/it/videos/numeri-complessi/addizione-sottrazione-moltiplicazione/ ja: https://astra-ai.co/ja/videos/complex-numbers-ja/ja-chapter-22/ km: https://astra-ai.co/km/videos/complex-numbers/chapter-ca42f548/ ko: https://astra-ai.co/ko/videos/complex-numbers-ko/22/ lo: https://astra-ai.co/lo/videos/lo-67d3f518/lo-ca42f548/ lt: https://astra-ai.co/lt/videos/kompleksiniai-skaiciai/sudetis-atimtis-daugyba/ lv: https://astra-ai.co/lv/videos/kompleksie-skaitli/saskaitisana-atnemsana-reizinasana/ ms: https://astra-ai.co/ms/videos/complex-numbers/bab-28-matematik-asas/ ms-BN: https://astra-ai.co/ms-BN/videos/nombor-kompleks/bab-ca42f548/ mx: https://astra-ai.co/mx/videos/numeros-complejos/capitulo-22/ my: https://astra-ai.co/my/videos/my-67d3f518/my-ca42f548/ nl: https://astra-ai.co/nl/videos/complexe-getallen/optellen-aftrekken-vermenigvuldigen/ no: https://astra-ai.co/no/videos/komplekse-tall/addisjon-subtraksjon-multiplikasjon/ pl: https://astra-ai.co/pl/videos/liczby-zespolone/dodawanie-odejmowanie-mnozenie/ pt: https://astra-ai.co/pt/videos/numeros-complexos/adicao-subtracao-multiplicacao/ pt-TL: https://astra-ai.co/pt-TL/videos/numeros-complexos/capitulo-de-video-022/ ro: https://astra-ai.co/ro/videos/numere-complexe/adunare-scadere-inmultire/ sk: https://astra-ai.co/sk/videos/komplexne-cisla/kapitola-022/ sl: https://astra-ai.co/sl/videos/kompleksna-stevila/sestevanje-odstevanje-mnozenje/ sr: https://astra-ai.co/sr/videos/kompleksni-brojevi/poglavlje-022/ sv: https://astra-ai.co/sv/videos/komplexa-tal/addition-subtraktion-och-multiplikation/ th: https://astra-ai.co/th/videos/complex-numbers/bot-28-bok-lop-khun/ tr: https://astra-ai.co/tr/videos/karmas-k-say-lar/bolum-022/ uk: https://astra-ai.co/uk/videos/uk-topic-04/uk-chapter-28/ vi: https://astra-ai.co/vi/videos/vi-topic-04/vi-chapter-28/ zh-HK: https://astra-ai.co/zh-HK/videos/shuxue-kecheng-004/shuxue-zhang-028/ zh-TW: https://astra-ai.co/zh-TW/videos/complex-numbers/chapter-ca42f548/ --- # Addition, Subtraction, Multiplication > Addition, subtraction, multiplication of complex numbers follow straightforward rules in a+bi form. This chapter works each operation in turn. ## INTRODUCTION Addition, subtraction, and multiplication are basic arithmetic operations that allow for the processing of numerical and algebraic expressions. These operations are the foundation of all further mathematical concepts. ## ADDITION Addition is an operation in which we combine two or more numbers into a single total value (sum). ### RULES OF ADDITION: - **COMMUTATIVITY:** a + b = b + a - **ASSOCIATIVITY:** (a + b) + c = a + (b + c) - **EXISTENCE OF AN IDENTITY ELEMENT (NEUTRAL ELEMENT):** a + 0 = a (0 is the additive identity) Examples: - 5 + 3 = 8 - (-4) + 7 = 3 ## SUBTRACTION Subtraction is the inverse operation of addition, where we determine the difference between two numbers. ### RULES OF SUBTRACTION: - a – b ≠ b – a (subtraction is generally not commutative) - a – 0 = a (subtracting the additive identity) Examples: - 9 – 4 = 5 - (-3) – (-7) = -3 + 7 = 4 ## MULTIPLICATION Multiplication is an operation of repeated addition of the same number. ### RULES OF MULTIPLICATION: - **COMMUTATIVITY:** a × b = b × a - **ASSOCIATIVITY:** (a × b) × c = a × (b × c) - **DISTRIBUTIVITY OVER ADDITION:** a × (b + c) = (a × b) + (a × c) - **EXISTENCE OF AN IDENTITY ELEMENT (NEUTRAL ELEMENT):** a × 1 = a (1 is the multiplicative identity) - **PRODUCT WITH 0:** a × 0 = 0 Examples: - 4 × 3 = 12 - (-2) × 5 = -10 ## IMPORTANCE OF THESE OPERATIONS Addition, subtraction, and multiplication are key operations in solving equations, computational problems, and analyzing numerical relationships. ## CONCLUSION Addition, subtraction, and multiplication allow for the basic processing of numbers and are the foundation of all further mathematical operations. Their rules ensure consistency in calculations.