Question

Given any complex number C,then for any integer k,
i4k+1=

Answer 1

Answer on Question #58299 – Math – Complex Analysis

Question

Given any complex number $C$, then for any integer $k$, $i^{4k+1} =$

Solution

$$i^{4k+1} = i \cdot i^{4k} = i \cdot (i^2)^k \cdot (i^2)^k = i \cdot (-1)^k \cdot (-1)^k = i \cdot (-1)^{2k} = i \cdot 1 = i.$$

Answer: $i$

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