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Powers of i quiz

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  • What is the value of i to the first power?
    i to the first power is just i.
  • What is i squared equal to?
    i squared is equal to -1.
  • How do you calculate i cubed using properties of exponents?
    i cubed is i squared times i, which equals -1 times i, or -i.
  • What is the value of i to the fourth power?
    i to the fourth power is 1.
  • What pattern do the powers of i follow?
    The powers of i cycle through four values: i, -1, -i, and 1.
  • What is i to the fifth power equal to?
    i to the fifth power is equal to i.
  • How can you simplify i to the sixth power?
    i to the sixth power is -1.
  • What is the value of i to the seventh power?
    i to the seventh power is -i.
  • How do you find the value of i to a high power, like i to the 100th?
    Check if the exponent is divisible by 4; if so, the result is 1.
  • What is the shortcut for evaluating i to any power?
    Divide the exponent by 4 and use the remainder to determine the value: 1 (i), 2 (-1), 3 (-i), or 0 (1).
  • If the exponent of i is not divisible by 4, what should you do?
    Divide the exponent by 4 and use the remainder to find the equivalent lower power of i.
  • What is i to the 22nd power?
    i to the 22nd power is -1.
  • How do you evaluate i to the 67th power?
    Divide 67 by 4 to get a remainder of 3, so i to the 67th power is -i.
  • What are the only possible results when evaluating any power of i?
    The only possible results are i, -1, -i, or 1.
  • Why is i to the fourth power important when simplifying higher powers of i?
    Because i to the fourth power equals 1, it allows you to reduce higher powers of i to one of four possible values.