Complex numbers and complex planes

Complex numbers and complex planes

Now that we know the basics of imaginary numbers, let's expand our knowledge and learn about another concept that is closely tied to imaginary numbers – complex numbers, a number that is consisted of a real part, and an imaginary part. In this section, we will learn what makes up a complex number, as well as how to plot on a complex plane.
Basic concepts: Evaluating and simplifying radicals, Solving quadratic equations using the quadratic formula, Nature of roots of quadratic equations: The discriminant,
Related concepts: Imaginary zeros of polynomials,

Lessons

  • Introduction
  • 1.
    For the following quadratic equations,
    i) find and classify the roots
    ii) plot the roots on the complex plane
    a)
    y=x2−1 y=x^2-1

    b)
    y=x2+1 y=x^2+1

    c)
    y=−x2+2x−5 y=-x^2+2x-5

  • 2.
    Given that function f(x)=2x2−2x+3 f(x)=2x^2-2x+3 , find the roots of the function
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46.
Imaginary and Complex Numbers
46.1
Introduction to imaginary numbers
46.2
Complex numbers and complex planes
46.3
Adding and subtracting complex numbers
46.4
Complex conjugates
46.5
Multiplying and dividing complex numbers
46.6
Distance and midpoint of complex numbers
46.7
Angle and absolute value of complex numbers
46.8
Polar form of complex numbers
46.9
Operations on complex numbers in polar form
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