Question

Find the value of the expression 1 + i^2+ i^4 +i^6 + i^8+...+i^20.​

Answer 1

Answer:

i^7665093/6-12

Step-by-step explanation:

cause if its like 28 than

Answer 2

Answer:

The given expression is :

1 + i^2+ i^4 +i^6 + i^8+...+i^20

to find it's value we must simplify the terms given,

we know that i=root(-1)

so,

i^2= -1,

i^4=(i^2)^2=(-1)^2=1,

i^6=(i^2)^3=(-1)^3=-1,

i^8=(i^2)^4=(-1)^4=1,

i^20=(i^2)^10=(-1)^10=1,

NOW

=> 1 + i^2+ i^4 +i^6 + i^8+...+i^20

= 1+(-1) +1+(-1) +1+(-1)+...+1+(-1)+1

= [1+(-1)] +[1+(-1)] +[1+(-1)]+...+[1+(-1)]+1

= 5[1+(-1)] + 1                                {as there are 11 terms}

= 5(0) + 1

= 1

Thus, the value of the given equation is 1