Teach complex numbers as geometry and transformations (not just algebra) with this Complex Plane and Transformations Workbook for Grades 11–12 (Algebra 2 / Precalculus). Students learn to see (a + bi) as a point/vector, understand addition as translation, multiplication by i as rotation, and modulus as distance—building the conceptual foundation that makes later polynomial and complex-root topics easier.

The workbook is organized into 4 focused chapters, each with Key Ideas + 20 exercises, followed by a full solutions section and a quick-reference page.

• Chapter 1 builds plotting fluency and conjugate symmetry in the complex plane.
• Chapter 2 treats complex numbers as vectors and teaches translation through addition/subtraction (component-wise).
• Chapter 3 makes rotation concrete: multiplying by i maps (a, b) → (−b, a) (a 90° counterclockwise rotation), with extensions to i^2, i^3, i^4.
• Chapter 4 builds modulus and distance: |a + bi| = sqrt(a^2 + b^2) and dist(z1, z2) = |z1 − z2|, including locus descriptions like |z| = 3.

Topics Covered (content)

• Plotting (a + bi), real/imag parts, conjugates
• Translation by addition (vector interpretation)
• Rotation by multiplying by i (90° CCW)
• Modulus as distance; distance between complex numbers; loci

Included Features

• 4 chapters (20 problems each) + quick reference + full worked solutions

Perfect for

• Grades 11–12 Algebra 2/Precalculus lessons, homework, review, and test prep on complex-plane geometry.