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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14.
Complex Numbers and Complex Plane
14.1
Introduction to imaginary numbers
14.2
Complex numbers and complex planes
14.3
Adding and subtracting complex numbers
14.4
Complex conjugates
14.5
Multiplying and dividing complex numbers
14.6
Distance and midpoint of complex numbers
14.7
Angle and absolute value of complex numbers
14.8
Polar form of complex numbers
14.9
Operations on complex numbers in polar form
Precalculus
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