Step 1: Find reference angle alpha = arctan(|b/a|) where z = a + ib

Step 2: Determine 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:

• Positive real axis: arg = 0
• Negative real axis: arg = pi
• Positive imaginary axis: arg = pi/2
• Negative imaginary axis: arg = -pi/2
• Origin: undefined

Operation Rules:

• arg(z1*z2) = arg(z1) + arg(z2), adjusted to (-pi, pi]
• arg$\frac{z1}{z2}$ = arg(z1) - arg(z2), adjusted
• arg(z-bar) = -arg(z)
• arg($z^n$) = n*arg(z), adjusted

Common Errors:

1. Forgetting to check the quadrant (getting pi/3 instead of -2*pi/3)
2. Not adjusting the sum/difference to (-pi, pi]
3. Confusing arg(-1) = pi with arg(-1) = -pi (pi is correct)
4. Using arg(z1+z2) = arg(z1) + arg(z2) (this is FALSE for addition)

JEE Tip: When computing arg of a quotient or product, compute individual arguments first, then add/subtract. Avoid computing the actual quotient/product when only the argument is needed.