https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:imaginary/v/introduction-to-i-and-imaginary-numbers 2023-08-11T18:51:22.662895381Z Intro to the imaginary numbers Learn about the imaginary unit, "i", a unique number defined as the square root of -1. It's a key part of complex numbers, which are in the form a + bi. The powers of "i" cycle through a set of values. Sal Khan video https://cdn.kastatic.org/googleusercontent/lAoqBYwnf7V4l_zYfB-33HtjhyHArhWHsitTAOeZHIrmEY8KF4AbLinF2iP3Xm3O2cYbD5-a2kgXkThLsHRIDxZS Intro to the imaginary numbers Learn about the imaginary unit, "i", a unique number defined as the square root of -1. It's a key part of complex numbers, which are in the form a + bi. The powers of "i" cycle through a set of values. https://cdn.kastatic.org/ka-youtube-converted/ysVcAYo7UPI.mp4/ysVcAYo7UPI.mp4 320 The imaginary unit i https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:imaginary/a/intro-to-the-imaginary-numbers 2021-06-30T17:32:36Z Intro to the imaginary numbers Learn about the imaginary unit i, about the imaginary numbers, and about square roots of negative numbers. article https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:imaginary/v/imaginary-roots-of-negative-numbers 2023-08-11T18:51:22.662895381Z 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 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/s03qez-6JMA.mp4/s03qez-6JMA.mp4 244 The imaginary unit i https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:imaginary/e/simplify-square-roots-of-negative-numbers 2025-03-01T15:52:37.13987578Z Simplify roots of negative numbers Rewrite square roots of negative numbers as imaginary numbers. Sulinya Ramanan exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:imaginary/a/powers-of-the-imaginary-unit 2021-06-30T17:32:34Z Powers of the imaginary unit Learn how to simplify any power of the imaginary unit i. For example, simplify i²⁷ as -i. article https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:imaginary/v/calculating-i-raised-to-arbitrary-exponents 2023-08-11T18:51:22.662895381Z 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 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/QiwfF83NWNA.mp4/QiwfF83NWNA.mp4 380 The imaginary unit i https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:imaginary/e/imaginary_unit_powers 2025-03-01T15:52:37.13987578Z Powers of the imaginary unit Simplify expressions with base i (the imaginary unit) raised to a positive exponent. Sulinya Ramanan exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:imaginary/v/i-as-the-principal-root-of-1-a-little-technical 2023-08-11T19:08:19.626529492Z i as the principal root of -1 The video explores the intriguing concept of imaginary numbers, specifically the imaginary unit 'i'. 'i' is equal to the square root of -1, and every complex number can be expressed as a + bi, where a and b are real numbers. This video clarifies misconceptions about square roots of negative numbers. Sal Khan video https://cdn.kastatic.org/googleusercontent/mGPU4gyFUucA-NevDHUsCQfcOZ0vm6yMUNHIPancC8N-Won5GPYWrAkh3ehJz7IIaVrExIPNrTfyKssQzh-OLJQ i as the principal root of -1 The video explores the intriguing concept of imaginary numbers, specifically the imaginary unit 'i'. 'i' is equal to the square root of -1, and every complex number can be expressed as a + bi, where a and b are real numbers. This video clarifies misconceptions about square roots of negative numbers. https://cdn.kastatic.org/ka-youtube-converted/rYG1D5lUE4I.mp4/rYG1D5lUE4I.mp4 404 The imaginary unit i