Question

Evaluate
${i}^{116}$
​

Answer 1

Given to evaluate -

$\sf{ i ^ { 116 } } \\ \\ \sf{ Thus \: can \: be \: written \: as \: - } \\ \\ \sf{ ( i ^ 2 ) ^ { 58 } } \\ \\ \sf{ Now , \: we \: know \: that \: - } \\ \\ \sf{ i ^ 2 = -1 } \\ \\ \sf{ \implies { ( -1 ) ^ 58 }} \\ \\ \sf{ \implies { 1 } }$

This is the required answer .

AddiTiOnaL InFoRmAtIon -

• $\sf{ i = \sqrt { -1 } }$

• $\sf{ i ^ 2 = -1 }$

$\sf{ i^4 = 1 }$

$\sf{ i^4 k= 1 }$

$\sf{ i ^ { ( 4k + 1 ) } = i }$

[tex] \sf{ i ^ { ( 4k + 2 ) } = -1 } [/tex ]

[ tex] \sf{ i ^ { ( 4k + 3 ) } = -i } [/tex ]

[ tex] \sf{ i ^ { ( 4k + 4 ) } = 1 } [/tex ]

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