Simplify and evaluate the following constant sums.
a. (i) Find a simplified expression, in terms of m, for k=1∑m+57, where m is a positive integer.
b. (ii) Hence determine k=1∑m+57−k=1∑m−27 and express your answer in the simplest form in terms of m.
c. (iii) Using your result from part (ii), calculate the value of the expression when m=12.