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Complex Numbers definitions

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  • Complex Number
    An expression combining a real value and an imaginary value, always written in the form a+bi.
  • Standard Form
    A representation where the real and imaginary parts are written as a+bi, with a and b as real numbers.
  • Real Part
    The component in a complex expression not multiplied by the imaginary unit, often denoted as 'a'.
  • Imaginary Part
    The coefficient of the imaginary unit in a complex expression, often denoted as 'b'.
  • Imaginary Unit
    A mathematical symbol, usually 'i', defined so that its square equals negative one.
  • I Squared
    A value resulting from multiplying the imaginary unit by itself, always equal to negative one.
  • Complex Conjugate
    A related expression formed by reversing the sign of the imaginary part in a complex number.
  • Addition
    A process where real and imaginary components of two complex expressions are combined separately.
  • Subtraction
    A process where real and imaginary components of two complex expressions are separated and then combined.
  • Multiplication
    An operation using distribution or FOIL, often resulting in an I squared term that simplifies to a real value.
  • FOIL Method
    A technique for multiplying two binomials, applied to complex expressions to expand and combine terms.
  • Distribution
    A method for multiplying a single term across a binomial, used in complex number operations.
  • Division
    A process involving multiplication by a conjugate to eliminate the imaginary unit from the denominator.
  • Fraction
    A form resulting from division, often split into real and imaginary parts with a common denominator.
  • Like Terms
    Components in complex expressions that share the same unit, allowing for combination during operations.