Introduction to imaginary numbers

Introduction to imaginary numbers

Have you ever run into a situation where you want to find the square root of a negative number, but the calculator gives you nothing but a big error? Well, we will explore the meaning of this error from a different perspective. In this section, we will introduce the notion of imaginary numbers, and how to simplify them.
Basic Concepts: Converting radicals to mixed radicals, Product rule of exponents, Power of a product rule
Related Concepts: Imaginary zeros of polynomials

Lessons

  • 1.
    Simplify the roots of negative numbers

    ■\blacksquare\; −16\sqrt{-16}
    ■\blacksquare\; −40\sqrt{-40}
    ■\blacksquare\; (−9)32(-9)^{\frac{3}{2}}
  • 2.
    Simplify the following imaginary numbers with high powers

    ■\blacksquare\; i5i^5
    ■\blacksquare\; i200i^{200}
    ■\blacksquare\; (3i2)4(\frac{3i}{2})^4
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15.
Complex Numbers and Complex Plane
15.1
Introduction to imaginary numbers
15.2
Complex numbers and complex planes
15.3
Adding and subtracting complex numbers
15.4
Complex conjugates
15.5
Multiplying and dividing complex numbers
15.6
Distance and midpoint of complex numbers
15.7
Angle and absolute value of complex numbers
15.8
Polar form of complex numbers
15.9
Operations on complex numbers in polar form
Precalculus
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