What is #i^1234# equivalent to?

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Answer 1 · 2015-11-24T14:28:30

#i^1234=-1#

To find out what #i# is equal to, divide the exponent by #4#.

Case 1: If the remainder is #0#, then it is equal to #1#.

Case 2: If the remainder is #1#, then it is equal to #i# or #sqrt(-1)#.

Case 3: If the remainder is #2#, then it is equal to #-1#.

Case 4: If the remainder is #3#, then it is equal to #-i# or #-sqrt(-1)#.

Solution

#" "1234/4=308 " remainder: " 2#

Therefore, we use case 3. #color(blue)(i^1234=-1)#