Question

Write the value of i38​

Answer 1

Answer:

-1

Step-by-step explanation:

Let's see what happens if we compute any power of

i

:

i

=

i

i

2

=

−

1

i

3

=

i

2

⋅

i

=

−

1

⋅

i

=

−

i

i

4

=

i

2

⋅

i

2

=

−

1

⋅

(

−

1

)

=

1

i

5

=

i

4

⋅

i

=

1

⋅

i

=

i

... and so on, after that, the sequence

i

,

−

1

,

−

i

and

1

repeats itself.

=================

How can you determine which one it is for

i

38

?

Let's start with factorizing

38

=

4

⋅

9

+

2

:

i

38

=

i

4

⋅

9

+

2

=

i

4

⋅

9

⋅

i

2

=

(

i

4

)

9

⋅

i

2

=

1

9

⋅

(

−

1

)

=

−

1

Answer 2

i38 = -1

Ｓｒａｖｓ Ｈｅｒｅ❣️

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