https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:complex-numbers-and-quadratic-equations-ncert-new/x808831787a7b08a2:algebra-of-complex-numbers/v/adding-complex-numbers 2025-01-07T14:22:35.748578099Z सम्मिश्र संख्याओं को जोड़ना (Adding complex numbers) Learn how to break down the process of adding complex numbers into simple steps. First, add the real parts. Then, do the same with the imaginary parts. The result? A new complex number! Learn and try some examples with Sal. Sal Khan video https://cdn.kastatic.org/googleusercontent/Wd8kN-oLGMV0Foadohf0YD4Z9K86EmTTsF0pzc5LUQU9u8Vqa5ztDLQWo_CFeeUFoNqrvHqHfyKGB65QBT3Ds_BK सम्मिश्र संख्याओं को जोड़ना (Adding complex numbers) Learn how to break down the process of adding complex numbers into simple steps. First, add the real parts. Then, do the same with the imaginary parts. The result? A new complex number! Learn and try some examples with Sal. https://cdn.kastatic.org/ka-youtube-converted/I4kaDaDoais.mp4/I4kaDaDoais.mp4 71 सम्मिश्र संख्याओं का बीजगणित (Algebra of complex numbers) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:complex-numbers-and-quadratic-equations-ncert-new/x808831787a7b08a2:algebra-of-complex-numbers/v/subtracting-complex-numbers 2025-02-03T14:16:00.002891013Z सम्मिश्र संख्याओं को घटाना (Subtracting complex numbers) Learn how to break down the process of subtracting complex numbers into simple steps. Distribute the negative sign to get rid of parentheses, then add up the real and imaginary parts separately. Voila! You've got your answer in the form of a + bi. Sal Khan video https://cdn.kastatic.org/googleusercontent/qNpLikDP9UKJlyiBToKSd1KwFsd7YGm9xnsNSZTvYI8POpXSwN2I-fgFKXoceCwe_wVZx9R-9IAF0FFHvb9llUSJ सम्मिश्र संख्याओं को घटाना (Subtracting complex numbers) Learn how to break down the process of subtracting complex numbers into simple steps. Distribute the negative sign to get rid of parentheses, then add up the real and imaginary parts separately. Voila! You've got your answer in the form of a + bi. https://cdn.kastatic.org/ka-youtube-converted/tt5_V9l8jdA.mp4/tt5_V9l8jdA.mp4 113 सम्मिश्र संख्याओं का बीजगणित (Algebra of complex numbers) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:complex-numbers-and-quadratic-equations-ncert-new/x808831787a7b08a2:algebra-of-complex-numbers/e/adding_and_subtracting_complex_numbers 2025-03-24T05:52:22.847271672Z सम्मिश्र संख्याओं को जोड़ें और घटाएं। सम्मिश्र संख्याओं (complex numbers) को जोड़ने और घटाने से संबंधित प्रश्नों का अभ्यास करें। Sulinya Ramanan exercise https://hi.khanacademy.org/math/class-12-bridge/x09646558c1ff0797:trigonometry-and-complex-numbers/x09646558c1ff0797:quadratic-equations-complex-numbers-linear-inequalities/v/multiplying-complex-numbers 2025-02-03T14:16:00.002891013Z सम्मिश्र संख्याओं का गुणन (Multiplying complex numbers) Discover how to multiply complex numbers! Just like multiplying regular numbers, you can use the distributive property or FOIL method. Remember, the imaginary unit 'i' squared equals -1. So, when you multiply complex numbers like 1-3i and 2+5i, you get a new complex number: 17-i. Sal Khan video https://cdn.kastatic.org/googleusercontent/pZb74VD7tUGU_ni69fUn6kHlXN04LuJ1R9gmcoVkzkTNsbb7Ju_fzSA6lxeBH8YPZIq7b-oGxhpF3Cit5dV7L2k सम्मिश्र संख्याओं का गुणन (Multiplying complex numbers) Discover how to multiply complex numbers! Just like multiplying regular numbers, you can use the distributive property or FOIL method. Remember, the imaginary unit 'i' squared equals -1. So, when you multiply complex numbers like 1-3i and 2+5i, you get a new complex number: 17-i. https://cdn.kastatic.org/ka-youtube-converted/Uu9MvtfE2gE.mp4/Uu9MvtfE2gE.mp4 332 सम्मिश्र संख्याओं का बीजगणित (Algebra of complex numbers) https://hi.khanacademy.org/math/class-12-bridge/x09646558c1ff0797:trigonometry-and-complex-numbers/x09646558c1ff0797:quadratic-equations-complex-numbers-linear-inequalities/e/multiply-complex-numbers-by-real-or-imaginary-numbers 2025-03-24T05:52:22.847271672Z सम्मिश्र संख्याओं का गुणन (आरंभिक स्तर) सम्मिश्र संख्याओं का गुणन एकल पद से कीजिए जो या तो वास्तविक (real) या शुद्ध काल्पनिक (pure imaginary) हैं| Sulinya Ramanan exercise https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:complex-numbers-and-quadratic-equations-ncert-new/x808831787a7b08a2:algebra-of-complex-numbers/e/multiplying_complex_numbers 2025-03-24T05:52:22.847271672Z सम्मिश्र संख्याओं का गुणन दो सम्मिश्र संख्याएं दी गई हैं, उनका गुणनफल ज्ञात कीजिए| Michal Pokorny exercise https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:complex-numbers-and-quadratic-equations-ncert-new/x808831787a7b08a2:algebra-of-complex-numbers/v/dividing-complex-numbers 2021-06-14T16:27:49Z सम्मिश्र संख्याओं का भाग (Dividing complex numbers) Sal divides (6+3i) by (7-5i). Sal Khan video https://cdn.kastatic.org/googleusercontent/v6x3LjgscQXXRr3vMbXZz2VTQ6zEco0MLDv2D-Ub-f9Kxw6SH_HZhnVR5Wm6tCGNCnOp0N-xEW4XlF8Y_rEaKkpU सम्मिश्र संख्याओं का भाग (Dividing complex numbers) Sal divides (6+3i) by (7-5i). https://cdn.kastatic.org/ka-youtube-converted/IV7fGP0-QHA.mp4/IV7fGP0-QHA.mp4 298 सम्मिश्र संख्याओं का बीजगणित (Algebra of complex numbers) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:complex-numbers-and-quadratic-equations-ncert-new/x808831787a7b08a2:algebra-of-complex-numbers/e/dividing_complex_numbers 2025-03-24T05:52:22.847271672Z सम्मिश्र संख्याओं का भाग (Divide complex numbers) एक सम्मिश्र संख्या विभाजन (complex number division) को देखते हुए, परिणाम को a+bi के रूप में एक सम्मिश्र संख्या के रूप में व्यक्त करें। Michal Pokorny exercise https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:complex-numbers-and-quadratic-equations-ncert-new/x808831787a7b08a2:algebra-of-complex-numbers/v/algebra-of-complex-numbers 2025-03-24T05:52:22.847271672Z सम्मिश्र संख्याओं का बीजगणित (Algebra of complex numbers) In this video, we talk about how we use operators in the complex world. We look at the properties of addition of complex numbers first. We then look which of these properties also hold true for subtraction. Then, we look at multiplication of complex numbers. Finally, we learn how to find the multiplicative inverse of a complex number. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw सम्मिश्र संख्याओं का बीजगणित (Algebra of complex numbers) In this video, we talk about how we use operators in the complex world. We look at the properties of addition of complex numbers first. We then look which of these properties also hold true for subtraction. Then, we look at multiplication of complex numbers. Finally, we learn how to find the multiplicative inverse of a complex number. https://cdn.kastatic.org/ka-youtube-converted/-d2MBb7nIH4.mp4/-d2MBb7nIH4.mp4 710 सम्मिश्र संख्याओं का बीजगणित (Algebra of complex numbers) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:complex-numbers-and-quadratic-equations-ncert-new/x808831787a7b08a2:algebra-of-complex-numbers/v/identities-involving-two-complex-numbers 2025-03-24T05:52:22.847271672Z दो सम्मिश्र संख्याओं को शामिल करने वाली सर्वसमिकाएँ (Identities involving two complex numbers) In this video, we look at a few algebraic identities involving squares and cubes of additon and subtraction of numbers. We realise that these identities work in a similar way in the complex world. We then prove one of these identities using laws of complex numbers (discussed in the previous video). We finally apply these identities to find cubes and other powers of addition and subtraction of two complex numbers. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw दो सम्मिश्र संख्याओं को शामिल करने वाली सर्वसमिकाएँ (Identities involving two complex numbers) In this video, we look at a few algebraic identities involving squares and cubes of additon and subtraction of numbers. We realise that these identities work in a similar way in the complex world. We then prove one of these identities using laws of complex numbers (discussed in the previous video). We finally apply these identities to find cubes and other powers of addition and subtraction of two complex numbers. https://cdn.kastatic.org/ka-youtube-converted/TqiKmYvXqzk.mp4/TqiKmYvXqzk.mp4 453 सम्मिश्र संख्याओं का बीजगणित (Algebra of complex numbers) https://hi.khanacademy.org/math/class-12-bridge/x09646558c1ff0797:trigonometry-and-complex-numbers/x09646558c1ff0797:quadratic-equations-complex-numbers-linear-inequalities/v/calculating-i-raised-to-arbitrary-exponents 2025-02-03T14:16:00.002891013Z काल्पनिक इकाई की घातें (Powers of the imaginary unit) The imaginary unit i is defined such that i²=-1. So what's i³? i³=i²⋅i=-i. What's i⁴? i⁴=i²⋅i²=(-1)²=1. What's i⁵? i⁵=i⁴⋅i=1⋅i=i. Discover how the powers of 'i' cycle through values, making it possible to calculate high exponents of 'i' easily. Sal Khan video https://cdn.kastatic.org/googleusercontent/iChCSFx4onWi8z32VteE3IuNrkNwD_Z65oEG5ixHAbFM5VZ2YlBKMON_WfRVontY13ohV4hbv8ZFToSUu52lI0GE काल्पनिक इकाई की घातें (Powers of the imaginary unit) The imaginary unit i is defined such that i²=-1. So what's i³? i³=i²⋅i=-i. What's i⁴? i⁴=i²⋅i²=(-1)²=1. What's i⁵? i⁵=i⁴⋅i=1⋅i=i. Discover how the powers of 'i' cycle through values, making it possible to calculate high exponents of 'i' easily. https://cdn.kastatic.org/ka-youtube-converted/mQF2OM6RjPI.mp4/mQF2OM6RjPI.mp4 380 सम्मिश्र संख्याओं का बीजगणित (Algebra of complex numbers) https://hi.khanacademy.org/math/class-12-bridge/x09646558c1ff0797:trigonometry-and-complex-numbers/x09646558c1ff0797:quadratic-equations-complex-numbers-linear-inequalities/e/imaginary_unit_powers 2025-03-24T05:52:22.847271672Z काल्पनिक इकाई की घातें (Powers of the imaginary unit) आधार i (काल्पनिक इकाई) के व्यंजकों को धनात्मक घातांक तक सरल करें| Sulinya Ramanan exercise https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:complex-numbers-and-quadratic-equations-ncert-new/x808831787a7b08a2:algebra-of-complex-numbers/v/imaginary-roots-of-negative-numbers 2025-02-03T14:16:00.002891013Z ऋणात्मक संख्याओं के मूलों को सरल करना (Simplifying roots of negative numbers) Discover the magic of the imaginary unit 'i'! This lesson dives into simplifying the square root of negative numbers using 'i', the principal square root of -1. We'll explore how to rewrite negative numbers as products, and use prime factorization to simplify roots. Sal Khan video https://cdn.kastatic.org/googleusercontent/ujHKobKRkpjNT4qHc8SHdhh_FhLy6vU3H8H7yIUyC0SpxGOHmyHfCWBTFM8fhtqUX92jop5dQFAgzkYMUzE_Bsll ऋणात्मक संख्याओं के मूलों को सरल करना (Simplifying roots of negative numbers) Discover the magic of the imaginary unit 'i'! This lesson dives into simplifying the square root of negative numbers using 'i', the principal square root of -1. We'll explore how to rewrite negative numbers as products, and use prime factorization to simplify roots. https://cdn.kastatic.org/ka-youtube-converted/KZNZlYqMB3w.mp4/KZNZlYqMB3w.mp4 244 सम्मिश्र संख्याओं का बीजगणित (Algebra of complex numbers) https://hi.khanacademy.org/math/up-math-class-11/x808831787a7b08a2:complex-numbers-and-quadratic-equations-ncert-new/x808831787a7b08a2:algebra-of-complex-numbers/e/simplify-square-roots-of-negative-numbers 2025-03-24T05:52:22.847271672Z ऋणात्मक संख्याओं के मूलों को सरल करना (Simplify roots of negative numbers) ऋणात्मक संख्याओं के वर्ग मूलों को काल्पनिक संख्याओं (imaginary numbers) के रूप में दोबारा से लिखिए। Sulinya Ramanan exercise