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Find the value of i^4 + i^5 + i^6 + i^7

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Find the value of i4 + i5 + i6 + i7

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i4 + i5 + i6 + i7 = (i2 )2 + i4 i + i4 .i2

Since, i = √−1, i 2 = −1, i3 = −i, i4 , = 1,

So, i4 + i5 + i6 + i7 =  (-1)2 + 1.i + 1(i) 2 + 1.(-i) 

= 1 +i+ 1 × -1 – i 

= 1 + i – 1 –i

 = 0

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