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)3 = 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