Printable Complex Solutions Worksheet | Grade 11 Algebra II

This worksheet teaches Algebra II students to solve quadratic equations that have complex solutions and then explain what those solutions mean in real situations. Students move from setting up a model to using the discriminant to decide whether a goal is reachable, justifying each conclusion in words.

At a Glance

• Grade: 11 · Subject: Algebra II
• Standard: HSN-CN.C.7 — Solve quadratics with complex solutions and say what they mean in context.
• Skill Focus: Interpreting complex solutions of a quadratic
• Format: 5 pages · 10 problems · Answer key included · PDF
• Best For: Applied practice after complex number instruction
• Time: 45–60 minutes

What's Inside

Five pages with a Key Ideas box, one worked example, and 10 tasks in three parts: direct models, multi-step applications, and constraint-based decisions. Contexts include projectile motion, area, revenue, AC circuits, and profit. A 3-page answer key shows full solutions.

Skill Progression

• Guided practice (Part A, 2 problems): Students write the model, solve it, and state the meaning, using the worked example as a template.
• Supported practice (Part B, 6 problems): Multi-step tasks lean on the Key Ideas box for the discriminant, conjugate pairs, and rounding rules.
• Independent practice (Part C, 2 problems): Students use the discriminant to choose between options and justify the choice in words.

The sequence follows gradual release: I Do, We Do, You Do.

Standards Alignment

HSN-CN.C.7 — Solve quadratic equations with real coefficients that have complex solutions. Tasks also ask students to interpret the discriminant and conjugate pairs. This standard code can be copied directly into lesson plans, IEP goals, or district curriculum mapping tools.

How to Use It

After direct instruction: assign Parts A and B in pairs as in-class practice, then save Part C for independent work. As review: use the full set as homework or a pre-assessment task. While students work, watch whether they check the discriminant before solving and whether they say that no real time, length, or price reaches the target. Expect 45 to 60 minutes for the full set, or 10 to 15 minutes for Part A alone.

Who It's For

Grade 11 Algebra II students who have learned the imaginary unit and the quadratic formula. Students who need support can start with Part A and the worked example, while Part C works as an extension. Pair it with a discriminant anchor chart for quick reference.

HSN-CN.C.7 asks students to solve quadratic equations with real coefficients that have complex solutions. This Grade 11 Algebra II worksheet turns that skill into 10 applied tasks across 5 pages, with a 3-page answer key. Students compute the discriminant, write solutions in a + bi form, and explain that a nonreal solution means no real time, length, or price reaches the target. The structure follows the gradual release model described by Fisher & Frey (2014), moving from a worked example and guided problems to independent decisions. Contexts such as projectile height, profit, area, and AC circuit impedance show why complex roots matter beyond symbolic manipulation. Teachers can use the worksheet in 45 to 60 minutes for practice after instruction, review, or formative assessment of whether students connect algebraic results to real-world meaning. Part C asks students to justify decisions in words.