Principal argument theta is in (-pi, pi].

Computing argument for z = a + ib:

1. Find reference angle alpha = arctan(|b/a|)
2. Adjust for quadrant:
   • Q1 (a>0, b>0): theta = alpha
   • Q2 (a<0, b>0): theta = pi - alpha
   • Q3 (a<0, b<0): theta = -(pi - alpha) = alpha - pi
   • Q4 (a>0, b<0): theta = -alpha

Special cases: arg(0) is undefined. arg(positive real) = 0. arg(negative real) = pi. arg(positive imaginary) = pi/2. arg(negative imaginary) = -pi/2.

Argument rules for operations:

• arg(z1*z2) = arg(z1) + arg(z2) (mod 2pi, adjust to principal range)
• arg$\frac{z1}{z2}$ = arg(z1) - arg(z2) (mod 2pi)
• arg(z-bar) = -arg(z)
• arg($z^n$) = n*arg(z) (mod 2pi)

Major pitfall: arg(z1*z2) = arg(z1) + arg(z2) may go outside (-pi, pi]. Always adjust the final answer to the principal range.