Editorial for Inaho VI
Submitting an official solution before solving the problem yourself is a bannable offence.
Without prior knowledge on the basics of complex numbers, this problem is impossible to solve. For example, it must be known that and that the rectangular coordinate form of a complex number is .
For the first subtask, since , we can utilize a simple if statement. If , the solution is . If , the solution is simply .
For the second subtask, some quick Googling will give the solutions to when and when . When , the solution is . When , the solution is . Alternatively, one can solve for when and manually using Euler's formula.
For the third subtask, one can utilize a for loop that iterates from to . Start with floating-point variables, set to , and set to . At each iteration of the for loop, it can be found that:
Alternatively, one can utilize a complex numbers library in their preferred programming language.
For the last subtask, one can figure out that solution converges to approximately , which means that after a certain , the solution becomes consistent up to decimal places. This means that we can hard code a value instead of looping up to . This certain and the proof is left as an exercise for the reader.