Question
Download Solution PDFThe value of i6 + i7 + i8, where \({\rm{i}} = \sqrt { - 1} \), is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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 i6 + i7 + i8
As we know, i2 = -1
So, i6 = i4 × i2 = 1 × -1 = -1
i7 = i4 × i3 = 1 × -i = -i
i8 = (i4)2 = (1)2 = 1
Now,
i6 + i7 + i8 = -1 - i + 1 = -i
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