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Question 2 (multiple answer)
Which simplifications of the powers of i are correct?

There is more than one correct answer. Select all correct answers.

i7=i4⋅i3=−1⋅−i=i
i6=i4⋅i2=1⋅−1=−1
i6=i4⋅i2=−1⋅−1=1
i7=i4⋅i3=1⋅−i=−i
i8=i4⋅i4=−1⋅−1=1
i5=i3⋅i2=−i⋅−1=i
i5=i3⋅i2=i⋅−1=−i
i8=i4⋅i4=1⋅1=1

Respuesta :

meerkat18
In mathematics, the roots or zeros of an equation could be real or complex. Complex roots are those that contain 'i' in their variables. This means that the root is imaginary so it cannot be plotted on a Cartesian plane. The equivalent of i is equal to √-1. So, when you take its square, i² = -1. Then, i³ = -i and i⁴ = 1. These are the important equalities you should know to simplify i raised to a very large number. All you have to do is partition the number in multiples of 2, 3 or 4 because they can be simplified. Taking note of these equalities, the correct operations are:

i6=i4⋅i2=1⋅−1=−1
i7=i4⋅i3=1⋅−i=−i
i5=i3⋅i2=−i⋅−1=i
i8=i4⋅i4=1⋅1=1