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Powers of i definitions Flashcards

Powers of i definitions
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  • Imaginary Unit
    A mathematical concept defined as the square root of negative one, forming the basis for complex numbers.
  • Exponent
    A number indicating how many times a base, such as the imaginary unit, is multiplied by itself.
  • I Squared
    A value resulting from multiplying the imaginary unit by itself, yielding negative one.
  • I Cubed
    A value obtained by multiplying the imaginary unit three times, resulting in negative imaginary unit.
  • I to the Fourth Power
    A value achieved by multiplying the imaginary unit four times, always simplifying to one.
  • Cycle of Powers
    A repeating sequence of four values—imaginary unit, negative one, negative imaginary unit, and one—when raising the imaginary unit to increasing exponents.
  • Remainder
    The amount left after dividing an exponent by four, used to determine the simplified value of a high power of the imaginary unit.
  • Divisibility by Four
    A property checked to quickly determine if a power of the imaginary unit simplifies directly to one.
  • Complex Number
    A number composed of a real part and an imaginary part, with the imaginary part involving the imaginary unit.
  • Properties of Exponents
    Rules that allow manipulation and simplification of expressions involving repeated multiplication of the same base.
  • Simplification
    The process of reducing a high power of the imaginary unit to one of four possible values using patterns or division.
  • Negative Imaginary Unit
    A value represented as the opposite of the imaginary unit, occurring in the cycle of powers.
  • Long Division
    A method used to divide the exponent by four to find the remainder for simplifying powers of the imaginary unit.
  • Pattern Recognition
    The skill of identifying the repeating sequence in the powers of the imaginary unit to streamline calculations.