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6: Complex Numbers

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  • 6.1: Complex Numbers
    Although very powerful, the real numbers are inadequate to solve equations such as x2+1=0, and this is where complex numbers come in.
  • 6.2: Polar Form
    In the previous section, we identified a complex number z=a+bi with a point (a,b) in the coordinate plane. There is another form in which we can express the same number, called the polar form.
  • 6.3: Roots of Complex Numbers
    A fundamental identity is the formula of De Moivre with which we begin this section.
  • 6.4: The Quadratic Formula
    When working with real numbers, we cannot solve the quadratic formula if b24ac<0. However, complex numbers allow us to find square roots of negative numbers, and the quadratic formula remains valid for finding roots of the corresponding quadratic equation.
  • 6.E: Exercises

Thumbnail: Argument φ and modulus r locate a point in the complex plane. (CC BY-SA 3.0; Wolfkeeper via Wikipedia)


This page titled 6: Complex Numbers is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Ken Kuttler (Lyryx) via source content that was edited to the style and standards of the LibreTexts platform.

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