Suppose `n` is a natural number such that `|i + 2i^2 + 3i^3 +...... + ni^n|=18sqrt2` where `i` is the square root of `-1`. Then `n` is

Options

A. `9`
B. `18`
C. `36`
D. `72`

Answer

C

Explanation

`(c )` `S=i+2i^(2)+3i^(3)+…….+ni^(n)`………..`(i)`
`:. iS=i^(2)+2i^(3)+3i^(4)+…….+ni^(n-1)`…………`(ii)`
Subtracting, we get ,brgt `S(1-i)=i+i^(2)+i^(3)+………..+i^(n)-ni^(n+1)`
`=(i(1-i^(n)))/(1-i)-ni^(n+1)`
Now put the values of `n` and verify.