### Let ( mathbb{C} ) be the field of complex numbers and ( mathbb{R} ) the subfield of real numbers. Then ( mathbb{C} ) is a vector space over ( mathbb{R} ) with usual addition and multiplication for complex numbers. Let ( omega=-frac{1}{2}+i frac{sqrt{3}}{2} ). Define the ( mathbb{R} )-linear map [ f: mathbb{C} longrightarrow

Let ( mathbb{C} ) be the field of complex numbers and ( mathbb{R} ) the subfield of real numbers. Then ( mathbb{C} ) is a vector space over ( mathbb{R} ) with usual addition and multiplication for complex numbers. Let ( omega=-frac{1}{2}+i frac{sqrt{3}}{2} ). Define the ( mathbb{R} )-linear map [ f: mathbb{C} longrightarrow