https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:complex-num/v/complex-number-intro 2021-06-30T17:32:40Z Intro to complex numbers Sal explains how we obtain complex numbers by adding real numbers and imaginary numbers. Sal Khan video https://cdn.kastatic.org/googleusercontent/7tN8YGuxyxzZLZ7DKhh3-s09xfkvj143mtnuLCp0HW17zDrbTrtU76dVFlSg7OIgCDkTlBKp1HcFioIgEFhczsS4 Intro to complex numbers Sal explains how we obtain complex numbers by adding real numbers and imaginary numbers. https://cdn.kastatic.org/ka-youtube-converted/SP-YJe7Vldo.mp4/SP-YJe7Vldo.mp4 284 Complex Numbers and Quadratic Equations https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:complex-num/v/introduction-to-complex-numbers 2023-08-11T19:08:19.626529492Z Classifying complex numbers Dive into expressions involving the imaginary unit 'i', simplifying them to reveal the real and imaginary components. Learn how real and imaginary numbers are subsets of complex numbers and study how to classify numbers as real, pure imaginary, or complex. Sal Khan video https://cdn.kastatic.org/googleusercontent/koHc-CEjQcvT_ieuWyBC8CylVQ5vQU3SUpel8ONpbE6oDr2HhGjqRIVPvZ061nkiKbQZGsl6PJhp5Ku-cAIB_K87 Classifying complex numbers Dive into expressions involving the imaginary unit 'i', simplifying them to reveal the real and imaginary components. Learn how real and imaginary numbers are subsets of complex numbers and study how to classify numbers as real, pure imaginary, or complex. https://cdn.kastatic.org/ka-youtube-converted/A_ESfuN1Pkg.mp4/A_ESfuN1Pkg.mp4 279 Complex Numbers and Quadratic Equations https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:complex-mul/v/multiplying-complex-numbers 2023-08-25T17:33:50.463554978Z 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 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/cWn6g8Qqvs4.mp4/cWn6g8Qqvs4.mp4 332 Complex Numbers and Quadratic Equations https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-div/v/dividing-complex-numbers 2021-06-10T13:39:36Z Dividing complex numbers Sal divides (6+3i) by (7-5i). Sal Khan video https://cdn.kastatic.org/googleusercontent/v6x3LjgscQXXRr3vMbXZz2VTQ6zEco0MLDv2D-Ub-f9Kxw6SH_HZhnVR5Wm6tCGNCnOp0N-xEW4XlF8Y_rEaKkpU Dividing complex numbers Sal divides (6+3i) by (7-5i). https://cdn.kastatic.org/ka-youtube-converted/Z8j5RDOibV4.mp4/Z8j5RDOibV4.mp4 298 Complex Numbers and Quadratic Equations 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 Complex Numbers and Quadratic Equations 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 Complex Numbers and Quadratic Equations https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-abs-angle/v/absolute-value-of-a-complex-number 2021-06-10T13:39:36Z Absolute value of complex numbers Sal finds the absolute value of (3-4i). Sal Khan video https://cdn.kastatic.org/googleusercontent/eUsJi5lrcndSRNvZaT1KCC49L2SpdVo7w9LfSEaGFf_GCy230EIF-7a9xTwPYTJ-IpZ8quFkQ3BeFUUesxifXeI Absolute value of complex numbers Sal finds the absolute value of (3-4i). https://cdn.kastatic.org/ka-youtube-converted/yvzyC4VBpUU.mp4/yvzyC4VBpUU.mp4 213 Complex Numbers and Quadratic Equations https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-div/v/complex-conjugates-example 2023-07-18T22:48:45.033562364Z Complex number conjugates Through a guided example with 7 - 5i, this video explains how to find the conjugate of a complex number, which is simply changing the sign of the imaginary part. Multiplying a complex number by its conjugate results in a real number. This is useful for simplifying complex numbers and is similar to the difference of squares. Sal Khan video https://cdn.kastatic.org/googleusercontent/v3PFAYy3GEGtzKvQYmUn8Utca1REhVtAR_YGNYZa2A82SbS3qgZsC46NI4DlgCBX8VQCvB6UYGzVUPIdf6C5KCgK Complex number conjugates Through a guided example with 7 - 5i, this video explains how to find the conjugate of a complex number, which is simply changing the sign of the imaginary part. Multiplying a complex number by its conjugate results in a real number. This is useful for simplifying complex numbers and is similar to the difference of squares. https://cdn.kastatic.org/ka-youtube-converted/dbxJ6LD0344.mp4/dbxJ6LD0344.mp4 241 Complex Numbers and Quadratic Equations https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:complex-plane/v/plotting-complex-numbers-on-the-complex-plane 2023-08-11T19:08:19.626529492Z Plotting numbers on the complex plane Understand the roles of real and imaginary parts in forming coordinates. Learn how to plot complex numbers on a unique two-dimensional grid known as the complex plane. Discover the real and imaginary parts of complex numbers, and see how they correspond to the horizontal and vertical axes.  Sal Khan video https://cdn.kastatic.org/googleusercontent/YlYYGjIobO5cH3JrocGa8zYOyLGBYvNVxzA4r28y3-dKcgPzkAYCvXY_e_79IurKEk1UmG7jB9YgsvftGs8Y5ns Plotting numbers on the complex plane Understand the roles of real and imaginary parts in forming coordinates. Learn how to plot complex numbers on a unique two-dimensional grid known as the complex plane. Discover the real and imaginary parts of complex numbers, and see how they correspond to the horizontal and vertical axes.  https://cdn.kastatic.org/ka-youtube-converted/kGzXIbauGQk.mp4/kGzXIbauGQk.mp4 74 Complex Numbers and Quadratic Equations https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-polar/v/polar-form-complex-number 2023-07-27T01:47:53.920337803Z Polar & rectangular forms of complex numbers Learn how to convert a complex number from rectangular form to polar form. This video covers how to find the distance (r) and direction (theta) of the complex number on the complex plane, and how to use trigonometric functions and the Pythagorean theorem to make the conversion. Sal Khan video https://cdn.kastatic.org/googleusercontent/vZFfqAnOIlbYbJh2-igsCkvUZQjshVYCkqJZLyUciqZR2YvOapIqm-1KktF6TXfPxNkqNuzAmO47mdG0GdbjX30Q Polar & rectangular forms of complex numbers Learn how to convert a complex number from rectangular form to polar form. This video covers how to find the distance (r) and direction (theta) of the complex number on the complex plane, and how to use trigonometric functions and the Pythagorean theorem to make the conversion. https://cdn.kastatic.org/ka-youtube-converted/8RasCV_Lggg.mp4/8RasCV_Lggg.mp4 736 Complex Numbers and Quadratic Equations https://www.khanacademy.org/math/ka-revision-class-11-math/x64e5efbb29d87707:week-1-revision-ncert-class-11-math/x64e5efbb29d87707:complex-numbers-and-quadratic-equations-revision-ncert-class-11-math/e/revision-complex-numbers-and-quadratic-equations-ncert-class-11-math 2026-04-07T22:59:30.107127435Z Revision Complex Numbers and Quadratic Equations Practice problems for revision of Complex Numbers and Quadratic Equations. Satya Swaroop exercise