Khan Academy
Exponential Form to Find Complex Roots
Sal solves the problem x^3 = 1 for all real and complex roots using the exponential form of the complex number. He shows how the roots found in the exponential form are the same as those in a more traditional form of a complex number...
Khan Academy
Basic Complex Analysis
This video gives an excellent overview of the different representations of a complex number. First, Sal reviews a pictorial representation of a complex number as an Argand diagram, then shows how to find the modulus and the argument of a...
Welch Labs
Imaginary Numbers Are Real (Part 8: Math Wizardry)
How does the Fundamental Theorem of Algebra apply to equations with complex roots? Using recently learned concepts about the complex plane, learners determine all the complex roots of polynomials. They can find the same roots...
Welch Labs
Imaginary Numbers Are Real (Part 7: Complex Multiplication)
Multiplying complex numbers geometrically is complicated. Find an easier way with a short video that explains the process of multiplying complex numbers on the complex plane. The connection with the process and the angles and moduli...
Welch Labs
Imaginary Numbers Are Real (Part 6: The Complex Plane)
How do addition and subtraction work on the complex plane? A short video presentation provides a clue on how to add complex numbers geometrically. The video ends with four problems to determine the rules for multiplication on the...
Welch Labs
Imaginary Numbers Are Real (Part 5: Numbers are Two Dimensional)
If the square root of negative one exists, where is it on the number line? A math video presents a geometric representation of complex numbers and the complex plane, and then compares it to the geometric representation of real...
Curated OER
How Do You Graph Complex Numbers?
Complex numbers have two parts and can be graphed on a complex plane. After an explanation of the complex plane, this video shows three examples of graphing complex numbers.
Khan Academy
Khan Academy: Algebra Ii: Complex Numbers: Imaginary and Complex Numbers
Video works through six problems from the California Standards Test. Three problems involve simplifying rational expressions, one of which uses exponent rules. Two problems involve graphing complex numbers or reading them from graphs....
Khan Academy
Khan Academy: Pre Calculus: Basic Complex Analysis
A video [13:04] introducing complex analysis. Complex numbers are defined as a number having two parts: a real part and an imaginary part. The instructor shows how to graph these in the complex number plane. The video also explains how...
Khan Academy
Khan Academy: Challenging Complex Numbers Problem (2 of 3)
This video lesson provides a challenging math problem that incorporates complex numbers. The question was taken from the Indian Institutes of Technology-Joint Entrance Examination (IIT-JEE).