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Multiplying and Dividing Complex Numbers definitions

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  • Complex Number
    A value expressed as a sum of a real part and an imaginary part, typically written in the form a+bi.
  • Imaginary Unit
    A special symbol, denoted as i, representing the square root of negative one and forming the basis for imaginary numbers.
  • Standard Form
    A way of writing a complex value as a sum of its real and imaginary parts, arranged as a+bi.
  • Complex Conjugate
    A value formed by changing the sign of the imaginary part of a complex number, keeping the real part unchanged.
  • FOIL Method
    A process for multiplying two binomials by multiplying First, Outside, Inside, and Last terms, then combining like terms.
  • Distribution
    A multiplication technique where each term in one expression is multiplied by every term in another.
  • I Squared
    A result equal to negative one, obtained when the imaginary unit is multiplied by itself.
  • Like Terms
    Parts of an expression that have the same variable components and can be combined through addition or subtraction.
  • Denominator
    The bottom part of a fraction, which in complex division often contains an imaginary term to be eliminated.
  • Numerator
    The top part of a fraction, which is multiplied by the complex conjugate during division.
  • Real Part
    The component of a complex value that does not involve the imaginary unit, represented by a in a+bi.
  • Imaginary Part
    The component of a complex value that is multiplied by the imaginary unit, represented by b in a+bi.
  • Exponent
    A number indicating how many times a value, such as the imaginary unit, is multiplied by itself.
  • Remainder
    The amount left after dividing the exponent of i by 4, used to determine the simplified value of high powers of i.