Question

iota power n+2 + iota power n+4​

Answer 1

Answer:

We have:

i^{n+1}i

n+1

+ i^{n+2}i

n+2

+ i^{n+3}i

n+3

+ i^{n+4}i

n+4

We have to find, the value of i^{n+1}i

n+1

+ i^{n+2}i

n+2

+ i^{n+3}i

n+3

+ i^{n+4}i

n+4

is:

Solution:

∴ i^{n+1}i

n+1

+ i^{n+2}i

n+2

+ i^{n+3}i

n+3

+ i^{n+4}i

n+4

= i^{n+1}i

n+1

+ i^{n+1}i

n+1

(i) + i^{n+1}i

n+1

(i^2i

2

) + i^{n+1}i

n+1

(i^3i

3

)

Taking i^{n+1}i

n+1

as common, we get

= i^{n+1}i

n+1

(1 + i + i^2i

2

+ i^3i

3

)

We know that,

i^{2}i

2

= - 1 and i^{3}i

3

= - i

= i^{n+1}i

n+1

(1 + i - 1 - i)

= i^{n+1}i

n+1

(0)

= 0

∴ i^{n+1}i

n+1

+ i^{n+2}i

n+2

+ i^{n+3}i

n+3

+ i^{n+4}i

n+4

= 0

Thus, the value of i^{n+1}i

n+1

+ i^{n+2}i

n+2

+ i^{n+3}i

n+3

+ i^{n+4}i

n+4

= 0

Answer 2

Answer:

KINDLY GO THROUGH THE ATTACHMENT

HOPE IT HELPS!