officerartola
contestada

The number i can be raised to whole number powers.

Look at the first four powers of i shown, and then use the drop-down menus to evaluate the expressions below.

The number i can be raised to whole number powers Look at the first four powers of i shown and then use the dropdown menus to evaluate the expressions below class=

Respuesta :

Answer:

[tex]i^{8}=1[/tex] and [tex]i^{34}=-1[/tex] will be the answer.

Step-by-step explanation:

Since i = [tex]\sqrt{(-1)}[/tex]

i² = (-1)

[tex]i^{3}=-i[/tex]

[tex]i^{4}=(-1)^{2}[/tex] = 1

[tex]i^{8}=1^{2}[/tex] = 1

[tex](i^{8})^{2}=1[/tex]

[tex]i^{34}=[i^{17}]^2[/tex]

     = [tex](i^{8}\times i^{8}\times i)^{2}[/tex]

     = [1 × 1 × √(-1)]²

     = 1² × 1² × [√(-1)]²

     = (-1)

Therefore, [tex]i^{8}=1[/tex] and [tex]i^{34}=-1[/tex] will be the answer.