imaginary number

  1. math_celebrity

    Find i^100

    i = sqrt(-1) i^2 = sqrt(-1)*sqrt(-1) = -1 i^3 = I^2 * I = -sqrt(-1) i^4 = I^2 * I^2 = -1 * -1 = 1 i^100 can be broken down. The easiest way is to check for powers of 4: 100 = 25 * 4 so we have: (i^4)^25 i^4 = 1, so we have: (i)^25 = 1
  2. math_celebrity

    −i × 2i × 3i

    (-1 x 2 x 3)(i x i x i) = 6i^3 -6i^3 = -6 x i^2 x I We know that i = sqrt(-1) i^2 = sqrt(-1) x sqrt(-1) i^2 = -1 -6(-1)(i) 6i
  3. math_celebrity

    if i = square root of -1 what is the sum (7 + 3i) + (-8 + 9i)

    if i = square root of -1 what is the sum (7 + 3i) + (-8 + 9i) We group like terms, and we get: 7 - 8 + (3 + 9)i Simplifying, we get: -1 + 12i
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