Question

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​Simplify and Express Answer

Answer 1

Answer:

-6i

Step-by-step 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

Answer 2

Step-by-step explanation:

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