Solving Complex Linear Problems on Vector Spaces

[cocobaby]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

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