CCSS HSN-CN.C.7 Worksheets
Algebra 2 · The Complex Number System
Solve quadratic equations with real coefficients that have complex solutions, writing the two conjugate roots in the form a + bi.
Below are free printable worksheets that support HSN-CN.C.7. Print them as PDFs, or generate a fresh one. Every math answer key is computed in code, so it is never wrong.
Teaching guide
What students learn
Solve quadratic equations with real coefficients that have complex solutions, writing the two conjugate roots in the form a + bi.
Worked example
Solve over the complex numbers: 2x² - 16x + 34 = 0. Write the solutions in a + bi form.
Answer: x = 4 + i or x = 4 - i
Why: a = 2, b = -16, c = 34. Discriminant = b² - 4ac = (-16)² - 4(2)(34) = 256 - 272 = -16 (negative, so the roots are non-real). = 4i. x = (-b ± √D) / (2a) = (16 ± 4i) / 4 = 4 + i or x = 4 - i.
Generated and checked in code, so it is correct.
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