1977 AHSME Problems/Problem 8
For every triple of non-zero real numbers, form the number . The set of all numbers formed is
Solution by e_power_pi_times_i
or depending whether is positive or negative. If , , and are positive, then the entire thing amounts to . If one of the three is negative and the other two positive, the answer is . If two of the three is negative and one is positive, the answer is . If all three are negative, the answer is . Therefore the set is .
This is very similar to https://artofproblemsolving.com/wiki/index.php/2017_AMC_8_Problems/Problem_21