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Introduction to Complex Numbers definitions

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  • Complex Number
    An expression combining a real part and an imaginary part, written in the form a+bi, where a and b are real numbers.
  • Imaginary Unit
    A special symbol, denoted as i, representing the square root of negative one and used to handle square roots of negative numbers.
  • Real Part
    The component of a complex number not multiplied by the imaginary unit, often denoted as a in a+bi.
  • Imaginary Part
    The coefficient of the imaginary unit in a complex number, represented by b in a+bi.
  • Standard Form
    The arrangement of a complex number as a+bi, with the real part first and the imaginary part second.
  • Radical
    A mathematical symbol indicating the root of a number, such as the square root, often used when simplifying negative roots.
  • Like Terms
    Terms in an expression that have the same variable or imaginary unit, allowing them to be combined through addition or subtraction.
  • Addition
    A process for combining complex numbers by adding their real parts and imaginary parts separately.
  • Subtraction
    A process for finding the difference between complex numbers by subtracting their real and imaginary parts separately.
  • Imaginary Number
    A number formed by multiplying a real number by the imaginary unit, such as 2i or 7i.
  • Coefficient
    A numerical factor multiplying the imaginary unit in a complex number, indicating the size of the imaginary part.
  • Simplification
    The process of rewriting expressions, such as square roots of negative numbers, in terms of the imaginary unit for clarity.
  • Expression
    A mathematical phrase that can include numbers, variables, and the imaginary unit, but does not contain an equals sign.
  • Negative Number
    A value less than zero, whose square root is not real and requires the use of the imaginary unit for evaluation.
  • Variable
    A symbol representing an unknown value, treated similarly to the imaginary unit when combining terms in complex numbers.