Question

`6i ^(955)`
​Simplify and Express Answer

Answer 1

Explanation:

`6 {i}^(955) = 6 {i}^(954 + 1) \\ \\ = 6 {i}^(954) * {i} \\ \\ = 6( {i}^(2) )^(477) * i \\ \\ = 6( - 1)^(477)* i ... (\because i^2 =-1)\\ \\ = 6 * ( - 1) * i\\... (\because 477\:is \: an \:odd \:number) \\ \\ = - 6i\\\\\huge \purple {\boxed {\therefore 6 {i}^(955) =-6i}}`

Answer 2

-6i

Explanation:

6×i⁹⁵⁵

Every fourth power of i is +1

i.e i⁴ = +1

i⁹⁵⁵ = i⁹⁵² × i³ (separating multiples of 4 in the power)

i⁹⁵² = +1 because 952 is multiple of 4

i⁹⁵⁵ = +1 × i³

i³ = -i

i⁹⁵⁵ = +1 × -i = -6

So,

6i⁹⁵⁵ = 6 × -i = -6i