Branches of multi-valued functions
General · Mathematics
Study notes
Q: Find both square roots of i. Describe the principal branch of log. √i: i = e^(iπ/2): roots e^(iπ/4), e^(i5π/4). e^(iπ/4) = (1+i)/√2. Other: -(1+i)/√2. Check: ((1+i)/√2)² = (1+2i+i²)/2 = 2i/2 = i ✓! Principal log: cut along negative real axis, -π < Arg ≤ π!