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Complex Numbers definitions

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  • Complex Number
    An expression in the form a + bi, combining a real part and an imaginary part, where i is the imaginary unit.
  • Real Part
    The component 'a' in a + bi, representing the non-imaginary value in a complex number.
  • Imaginary Part
    The coefficient 'b' in a + bi, indicating the value multiplied by the imaginary unit.
  • Imaginary Unit
    A mathematical constant denoted as i, defined by the property that i squared equals negative one.
  • Standard Form
    The arrangement of a complex number as a + bi, with the real part first and the imaginary part second.
  • Like Terms
    Terms in an expression that share the same variable component, such as those with or without the imaginary unit.
  • Complex Conjugate
    A related complex number formed by reversing the sign of the imaginary part in a + bi.
  • FOIL Method
    A technique for multiplying two binomials, applying multiplication to first, outside, inside, and last terms.
  • Distributive Property
    A rule allowing multiplication of a single term across terms within parentheses in an expression.
  • i Squared
    A value resulting from multiplying the imaginary unit by itself, always equal to negative one.
  • Quotient
    The result of dividing one complex number by another, often requiring rationalization of the denominator.
  • Rationalization
    A process of eliminating the imaginary unit from a denominator by multiplying by the complex conjugate.
  • Binomial
    An algebraic expression containing exactly two terms, such as a + bi.
  • Fraction Expansion
    The separation of a complex fraction into distinct real and imaginary parts, each with the same denominator.
  • Multiplicative Identity
    A property where multiplying by one leaves a number unchanged, used when multiplying numerator and denominator by the same value.