Mathematics
High School (11–12)
Algebra › Complex NumbersAlgebra › Quadratic EquationsChapter 3Contains Standard contentComplex Numbers and Quadratic Equations
The equation x squared plus 1 equals 0 has no real solution. Mathematicians did not give up: they invented a number i whose square is minus one, and a whole new world of numbers opened up. In this chapter you calculate with complex numbers, picture them as points on the Argand plane, find their modulus and conjugate, and solve every quadratic equation, even those with a negative discriminant. Python has complex numbers built in, so you can check every step.
Part of Mathematics · High School (11–12) (chapter 3)
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Complex Numbers and Their Algebra
Meet i, write numbers as a + ib, and add, subtract, multiply and divide them. Find powers of i, and the identities that still hold for complex numbers.
The Argand Plane and Quadratic Equations
Picture complex numbers as points, find their modulus and conjugate and what they mean on the plane, then solve quadratic equations with a negative discriminant and find square roots of complex numbers.