Compute the number of ordered pairs of integers (x,y) with \(1\le x such that \(i^x+i^y\) is a real number.
sorry, the latex seemed to have failed. this is the question:
Compute the number of ordered pairs of integers (x,y) with \(1\le x such that \(i^x+i^y\) is a real number.
+1223 Here are the powers of i:
i^0 = 1
i^1 = i
i^2 = -1
i^3 = -i
i^x + i^y is a real number if:
- x is divisible by 4 and y is 2 more than a multiple of 4
-x is 1 more than a multiple of 4 and y is 3 more than a multiple of 4
