- #1
aliciaislol
- 8
- 0
Homework Statement
Consider C^x, the multiplicative group of nonzero complex numbers, and let f:C^x --> C^x be defined by f(x)=x^4. Find ker f.
Homework Equations
C - complex numbers
e^i2xpi = cos theta + isin theta element oof C
R - reals
Z- integers
where R/Z
This is the equation we got in class:
ker f= {x element of R : f(x) =1} = {x element of R: e^(i2xpi)=1} = {x element of R: cos(2xpi) + isin(2xpi) =1} = Z
The Attempt at a Solution
Based on the above info:
ker f= {x element of C^x : f(x) =1} = {x element of C^x : (e^(i2xpi))^4 =1} = {x element of C^x : e^(i8xpi) =1} = {x element of C^x: cos(8xpi) + isin(8xpi) =1}
Am I doing this right? Is there an easier way?