Complex linear problem

1. Mar 8, 2010

cocobaby

1. The problem statement, all variables and given/known data

Let V be the set of all complex numbers regarded as a vector space over the field of real numvers. Find a function from V into V which is a linear transformation on the above vector space, but which is not a linear transformation on C1, i.e.,which is not complex linear.

2. Relevant equations

3. The attempt at a solution

2. Mar 8, 2010

HallsofIvy

Try $z\rightarrow \overline{z}$. That is, $(x, y)\rightarrow (x, -y)$.