Khan Academy: Algebra: Complex Numbers: Introduction to I and Imaginary Numbers

Students are always fascinated by imaginary numbers. In this video, Sal defines the imaginary unit, i, and shows when raising i to an exponent, it has a cyclic nature.

Video first reviews what imaginary and complex numbers are. Shows example of graphing a complex number. Gives general explanations and formulas for adding, subtracting, multiplying and dividing complex numbers. Includes link to...

Video shows working a problem from the IIT JEE test which involves using algebraic manipulation to determine the validity of an equation with magnitudes of the differences of certain complex numbers. [7:21]

Video shows working a problem from the IIT JEE test which involves algebraic manipulation and using what the argument of complex numbers is to visually reason if two given equations about arguments are true. [7:26]

Video shows working a problem from the IIT JEE test which involves determining whether the determinant of a matrix of four given complex numbers is 0. [3:09]

Video shows how to use the quadratic formula to find roots of a quadratic equation in a situation where the roots are complex. Includes showing how to verify the answers are correct solutions of the quadratic. [10:15]

Video shows an example of dividing complex numbers using complex conjugates. [4:58]

Video shows an example of multiplying complex numbers. [5:32]

Video shows an example of subtracting complex numbers. [1:53]

Video shows how to divide complex numbers by using complex conjugates in general terms and then with a specific example. [8:58]