Question

How do you find the sum of `11+4i` from i=1 to 45?

Answer 1

Sum of `11+4i` from `i=1` to `45` is `4635`

Explanation:

`11+4i`, where `i=1` to `45`, basically represents

an arithmetic series, whose first term is `11+4xx1=15` and common difference `d=4`, as subsequent terms go up by `4`

Hence sum of the series for `n` terms is given by

`S_n=n/2(2a+(n-1)d)`

and the sum of `11+4i` from `i=1` to `45` is

`S_(45)=45/2(2xx15+(45-1)xx4)`

= `45/2xx(30+44xx4)`

= `45/2(30+176)`

= `45/2xx206=4635`