Assignment:
Q1. Let b and d be distinct nonzero real numbers and c any real number .Prove that { b,c +di } is a basis of C over R.
Hint-For any r + si ∈ C, r +si= ( r/b-cs/bd)b +s/d(c+di).Hence {b,c + di} spans C over R. Prove that it is also linearly independent over R.
Q2. If a+bi ∈ C and b≠0 ,prove that C= R(a +bi).
C-complex
R-reals
Provide complete and step by step solution for the question and show calculations and use formulas.