Difference between revisions of "Complex Numbers"
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| − | A complex number is a number of the form <math> a + bi </math> where <math> a </math> is the real part of the complex number, and <math> bi </math> is the imaginary part of the complex number. The imaginary unit <math> i = \sqrt{-1}</math>, and can be used to express imaginary numbers (for example, <math> \sqrt{-25} = 5\sqrt{-1} = 5i </math>). | + | A complex number is a number of the form <math> a + bi </math> where <math> a </math> is the real part of the complex number, and <math> bi </math> is the imaginary part of the complex number. If <math> b = 0 </math>, then <math> a + bi </math> is a real number. If <math> a = 0 </math> and b is not equal to 0, the complex number is called an imaginary number. The imaginary unit <math> i = \sqrt{-1}</math>, and can be used to express other imaginary numbers (for example, <math> \sqrt{-25} = 5\sqrt{-1} = 5i </math>). <math> i^2 = -1 </math>, <math> i^3 = -i </math>, <math> i^4 = 1 </math>, <math> i^5 = i </math> again, and so on. |
==Resources== | ==Resources== | ||
* [https://tutorial.math.lamar.edu/classes/alg/ComplexNumbers.aspx Complex Numbers], Paul's Online Notes | * [https://tutorial.math.lamar.edu/classes/alg/ComplexNumbers.aspx Complex Numbers], Paul's Online Notes | ||
* [https://courses.lumenlearning.com/collegealgebra2017/chapter/introduction-complex-numbers/ Intro to Complex Numbers], Lumen Learning | * [https://courses.lumenlearning.com/collegealgebra2017/chapter/introduction-complex-numbers/ Intro to Complex Numbers], Lumen Learning | ||
Revision as of 13:02, 20 September 2021
A complex number is a number of the form where is the real part of the complex number, and is the imaginary part of the complex number. If , then is a real number. If and b is not equal to 0, the complex number is called an imaginary number. The imaginary unit , and can be used to express other imaginary numbers (for example, ). , , , again, and so on.
Resources
- Complex Numbers, Paul's Online Notes
- Intro to Complex Numbers, Lumen Learning
