Is this true
Hello, Im having problems with equivalence classes.
The relation R is defined for complex numbers z=x+yi and w=a+bi. zRw if and only if x+b=y+a
I am asked to give the elements of the equivalence class containg [i]
I have wrote, [i]={xeC:xRi}={xeC:x-i} to begin finding the equivalence classes, but am stuck trying to find the elements
The real numbers are a subset of the complex numbers. a+ib is a complex numbers, so imaginary numbers can be added or subtracted to the realnumber to form a complex number.
I know i^2 is -1
So the equivalence class containing i will just be those elements congruent to i? So the elements would be the complex numbers. Or is this chasing the wrong argument?