9.2.4.3

Recognize that to solve certain equations, number systems need to be extended from whole numbers to integers, from integers to rational numbers, from rational numbers to real numbers, and from real numbers to complex numbers. In particular, non-real complex numbers are needed to solve some quadratic equations with real coefficients.

Khan Academy Resources

Understanding the quadratic formulaIntro to complex numbersIntro to the imaginary numbersThe complex planeVisualizing complex number powersQuadratic formula reviewPowers of complex numbersQuadratic formulaPlot numbers on the complex planeSimplify roots of negative numbersSolve quadratic equations: complex solutionsParts of complex numbersClassify complex numbersFactor polynomials: complex numbersi as the principal root of -1Worked example: quadratic formula (negative coefficients)Simplifying roots of negative numbersSolving quadratic equations: complex rootsThe quadratic formulaWorked example: quadratic formula (example 2)Factoring polynomials using complex numbersPlotting numbers on the complex planeQuadratics & the Fundamental Theorem of Algebra Classifying complex numbersTaking and visualizing powers of a complex numberComplex numbers & sum of squares factorizationIntro to complex numbers

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