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The value of i12 + i13 + i14 + i15, where \({\rm{i}} = \sqrt { - 1} \), is
1. 1
2. - i 
3. - 1
4. 0

1 Answer

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Best answer
Correct Answer - Option 4 : 0

Concept:

Power of i:

  • i = \(\sqrt{-1}\)
  • i2 = -1
  • i3 = i × i2 = -i
  • i4 = (i2)2 = (-1)2 = 1
  • i4n = 1

 

Calculation:

To Find: Value of i12 + i13 + i14 + i15

As we know, i2 = -1

So, i12 = (i4)= 1

i13 = (i4)3 × i = 1 × i = i

i14 = (i4)3 × i2 = 1 × -1 = -1

i15 = (i4)3 × i3 = 1 × -i = -i

Now, 

i12 + i13 + i14 + i15  = 1 + i - 1 - i = 0

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