+0  
 
0
50
2
avatar

Compute the number of ordered pairs of integers (x,y) with \(1\le x  such that  \(i^x+i^y\) is a real number.

 Feb 26, 2021
 #1
avatar
0

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.

 Feb 26, 2021
 #2
avatar+939 
+1

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

 Feb 26, 2021

29 Online Users

avatar
avatar
avatar
avatar