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Imaginary and Complex Numbers in Precalculus

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Terms in this set (7)

  • Definition of the imaginary unit i
    The imaginary unit \(i\) is defined as \(i=\sqrt{-1}\), so \(i^2=-1\).
  • Definition of imaginary numbers
    Imaginary numbers are numbers involving \(i\), the square root of a negative number.
  • Definition of a complex number
    A complex number is of the form \(a+bi\), where \(a,b\) are real numbers and \(i=\sqrt{-1}\).
  • When is a complex number a real number?
    If \(b=0\), the complex number \(a+bi\) is a real number.
  • When is a complex number an imaginary number?
    If \(a=0\) and \(b\neq0\), the complex number is an imaginary number.
  • What are complex conjugates?
    The complex conjugates of \(a+bi\) and \(a-bi\) are called complex conjugates.
  • Why is i written outside the radical?
    i is written in front of the radical to avoid mistakenly placing it inside the radical.