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Question 1 of 5
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Imaginary numbers have the properties i0=1i0=1, i1=ii1=i, i2=-1i2=−1 and i3=-ii3=−i.
Use the formula i4n+ri4n+r to simplify the powers of the imaginary unit.
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i15i15 |
Divide the power 1515 by 44. This gives 33 with a remainder of 33. |
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i4×3+3i4×3+3 |
Rewrite using the formula i4n+ri4n+r where the n=3n=3 and the r=3r=3. |
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i12+3i12+3 |
Simplify |
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i12+3i12+3 |
The 33 means that this number is the same as i3=-ii3=−i. |
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-i−i |
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Question 2 of 5
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Imaginary numbers have the properties i0=1i0=1, i1=ii1=i, i2=-1i2=−1 and i3=-ii3=−i.
Use the formula i4n+ri4n+r to simplify the powers of the imaginary unit.
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i50i50 |
Divide the power 5050 by 44. This gives 1212 with a remainder of 22. |
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i4×12+2i4×12+2 |
Rewrite using the formula i4n+ri4n+r where the n=12n=12 and the r=2r=2. |
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i48+2i48+2 |
Simplify |
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i48+2i48+2 |
The 22 means that this number is the same as i2=-1i2=−1. |
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-1−1 |
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Question 3 of 5
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Imaginary numbers have the properties i0=1i0=1, i1=ii1=i, i2=-1i2=−1 and i3=-ii3=−i.
Use the formula i4n+ri4n+r to simplify the powers of the imaginary unit.
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i149i149 |
Divide the power 149149 by 44. This gives 3737 with a remainder of 11. |
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i4×37+1i4×37+1 |
Rewrite using the formula i4n+ri4n+r where the n=37n=37 and the r=1r=1. |
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i138+1i138+1 |
Simplify |
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i138+1i138+1 |
The 11 means that this number is the same as i1=ii1=i. |
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ii |
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Question 4 of 5
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Imaginary numbers have the properties i0=1i0=1, i1=ii1=i, i2=-1i2=−1 and i3=-ii3=−i.
Use the formula i4n+ri4n+r to simplify the powers of the imaginary unit.
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i20i20 |
Divide the power 2020 by 44. This gives 55 with a remainder of 00. |
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i4×5+0i4×5+0 |
Rewrite using the formula i4n+ri4n+r where the n=5n=5 and the r=0r=0. |
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i20+0i20+0 |
Simplify |
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i20+0i20+0 |
The 00 means that this number is the same as i0=1i0=1. |
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11 |
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Question 5 of 5
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Imaginary numbers have the properties i0=1i0=1, i1=ii1=i, i2=-1i2=−1 and i3=-ii3=−i.
Use the formula i4n+ri4n+r to simplify the powers of the imaginary unit.
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i37i37 |
Divide the power 3737 by 44. This gives 99 with a remainder of 11. |
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i4×9+1i4×9+1 |
Rewrite using the formula i4n+ri4n+r where the n=37n=37 and the r=1r=1. |
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i36+1i36+1 |
Simplify |
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i36+1i36+1 |
The 11 means that this number is the same as i1=ii1=i. |
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ii |
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