Find n.

Firstly,the co-efficient of i and the real part will both be integers...so if the mod is 18√2 then surely both parts'(real and imaginary) co-efficients are 18 itself....therefore...

co-efficient of i is (1-3+5-7+9....)..
the above sum upto n terms is equal to (-1)ⁿ⁺¹n...
therefore n here is 18..
now every 2 terms out of 4 are imaginary and the other two real...
therefore total no of terms(n to be calculated) is 36.

iⁿ can either be 1, -1 or i. The left side will be a natural number or a complex number, whereas the right side is irrational. Therefore there is no solution for n.