Mathematical constants | Algebraic numbers | Complex numbers | Quadratic irrational numbers
The imaginary unit or unit imaginary number (i) is a solution to the quadratic equation . Although there is no real number with this property, i can be used to extend the real numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of i in a complex number is . Imaginary numbers are an important mathematical concept; they extend the real number system to the complex number system , in which at least one root for every nonconstant polynomial exists (see Algebraic closure and Fundamental theorem of algebra). Here, the term "imaginary" is used because there is no real number having a negative square. There are two complex square roots of −1: i and , just as there are two complex square roots of every real number other than zero (which has one double square root). In contexts in which use of the letter i is ambiguous or problematic, the letter j or the Greek is sometimes used instead. For example, in electrical engineering and control systems engineering, the imaginary unit is normally denoted by j instead of i, because i is commonly used to denote electric current. (Wikipedia).
Imaginary numbers are any numbers that include the imaginary number i. A mix of imaginary and real numbers gives you what’s called a complex number. The primary reason we use imaginary numbers is to give us a way to find the root (radical) of a negative number. There’s no way to use real
From playlist Popular Questions
Tutorial - What is an imaginary number
http://www.freemathvideos.com In this video playlist you will learn everything you need to know with complex and imaginary numbers
From playlist Complex Numbers
Imaginary Numbers, Functions of Complex Variables: 3D animations.
Visualization explaining imaginary numbers and functions of complex variables. Includes exponentials (Euler’s Formula) and the sine and cosine of complex numbers.
From playlist Physics
We discuss what imaginary numbers are and how they are part of the larger set of complex numbers in this free math video tutorial by Mario's Math Tutoring. This is a nice introduction to working with i. We also go through some examples. 0:26 A Hierarchy of Different Types of Numbers 1:03
From playlist Imaginary & Complex Numbers
http://www.freemathvideos.com In this video series I will show you how to rewrite a number using i.
From playlist Simplify Rational Expressions
Imaginary Numbers Are Real [Part 10: Complex Functions]
Supporting Code: https://github.com/stephencwelch/Imaginary-Numbers-Are-Real More information and resources: http://www.welchlabs.com Imaginary numbers are not some wild invention, they are the deep and natural result of extending our number system. Imaginary numbers are all about the di
From playlist Imaginary Numbers are Real
Imaginary Numbers Are Real [Part 11: Wandering in 4 Dimensions]
More information and resources: http://www.welchlabs.com Supporting Code: https://github.com/stephencwelch/Imaginary-Numbers-Are-Real Imaginary numbers are not some wild invention, they are the deep and natural result of extending our number system. Imaginary numbers are all about the di
From playlist Imaginary Numbers are Real
Imaginary Numbers Are Real [Part 1: Introduction]
For early access to new videos and other perks: https://www.patreon.com/welchlabs Want to learn more or teach this series? Check out the Imaginary Numbers are Real Workbook: http://www.welchlabs.com/resources. Imaginary numbers are not some wild invention, they are the deep and natural
From playlist Imaginary Numbers are Real
Imaginary Numbers Are Real [Part 5: Numbers are Two Dimensional]
More information and resources: http://www.welchlabs.com Imaginary numbers are not some wild invention, they are the deep and natural result of extending our number system. Imaginary numbers are all about the discovery of numbers existing not in one dimension along the number line, but in
From playlist Imaginary Numbers are Real
Algebra - Ch. 0.6: Basic Concepts (2 of 36) What are Imaginary Numbers?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the differences between real and imaginary numbers on a number line, a real and imaginary axis, and the x-y plane. Next video in this series can be seen at: https://youtu.be/jqQXoh9YQQY
From playlist ALGEBRA 0.6 BASIC CONCEPTS
Complex Numbers - Powers of i | Don't Memorise
Calculating the powers of I gives us a very interesting result. Watch the video to know more about the unit imaginary number. ✅To access all videos related to Complex Numbers, enroll in our full course now: https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&utm_
From playlist Complex Numbers
Algebra 2 4.4e - Complex Numbers, Part 5 - The Imaginary Unit
What 'i' is, and the pattern that appears when raising i to a power. Part of the Algebra 2 series on complex numbers. By Derek Owens. Distance learning courses are available at http://www.derekowens.com
From playlist Algebra 2 - Complex Numbers
What is the difference between imanginary numbers and complex numbers
http://'www.freemathvideos.com In this math tutorial I will show you how write a complex number in standard form after simple operations have been performed. You will learn how to find the value of real and imaginary numbers in a complex number and then write it in standard form. To simp
From playlist Simplify Rational Expressions
Calculus 2: Complex Numbers & Functions (7 of 28) Geometric Representation of Addition & Subtraction
Visit http://ilectureonline.com for more math and science lectures! In this video I will show numerically the geometrical representation of a complex number and it modulus of (2+3i)+(3-i)=? and (2+3i)-(3-i)=? Next video in the series can be seen at: https://youtu.be/E30ZClLMYYg
From playlist CALCULUS 2 CH 11 COMPLEX NUMBERS
Algebra - Ch. 24: Complex Numbers (4 of 28) Imaginary Numbers & the Number Line
Visit http://ilectureonline.com for more math and science lectures! We will learn about the imaginary numbers and the number line. All real numbers are on the number line. All irrational numbers can be defined as being between 2 rational numbers. To donate: http://www.ilectureonline.com/
From playlist ALGEBRA CH 24 COMPLEX NUMBERS
[ANT07] Units and logarithm space (+ bonus theorems)
There are infinitely many units in Z[√2]. How can we write them down? How can we figure out their multiplicative structure? (Plus, now that we've come this far, a few theorems to make the link between this course and more traditional courses.)
From playlist [ANT] An unorthodox introduction to algebraic number theory
Algebra - Ch. 24: Complex Numbers (5 of 28) Complex Numbers & the Number Line
Visit http://ilectureonline.com for more math and science lectures! We will learn about complex numbers and the number line. Complex numbers=real numbers+imaginary line. To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 . Next video in this series can
From playlist ALGEBRA CH 24 COMPLEX NUMBERS
Why are complex numbers awesome? What are they and how are they useful? Free ebook http://bookboon.com/en/introduction-to-complex-numbers-ebook Test your understanding via a short quiz http://goo.gl/forms/3T2ZqTfgrL Make learning "complex" numbers easy through an interactive, fun and
From playlist Intro to Complex Numbers
PHYS 201 | Superposition 4 - Imaginary Axis
We can think of 1D sinusoidal motion as just 1 dimension of circular motion. No problem. We can even "imagine" that 1D sinusoidal motion is really circular motion where the object is also moving along an imaginary second axis. OK. But what if I showed you THAT WE CAN ALSO PROVE THAT MATHEM
From playlist PHYS 201 | Oscillators
How Imaginary Numbers Make Real Physics Easier to Understand
Go to Squarespace.com for a free trial, and when you’re ready to launch, go to http://www.squarespace.com/parthg to save 10% off your first purchase of a website or domain. #imaginarynumber #complexnumbers #physics In this video, we'll look at the basics of complex and imaginary numbers,
From playlist Quantum Physics by Parth G