Difference between revisions of "Complex Numbers"

From Department of Mathematics at UTSA
Jump to navigation Jump to search
Line 1: Line 1:
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.
+
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>).
  
 
==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 13:03, 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, ).

Resources