Florida B.E.S.T. MA.912.NSO.2

MathGrades 9–12

B.E.S.T. Standard (Benchmark Cluster)

Represent and perform operations with expressions within the complex number system.

Florida B.E.S.T. Standards for Mathematics

Cluster contents

MA.912.NSO.2 is a B.E.S.T. standard. These are the benchmarks under it.

Teacher's field guide

What Students Need to Do: Students write complex numbers in a + bi form and represent them on the complex plane. They add, subtract, multiply, and divide complex expressions while simplifying powers of i and using conjugates when needed.
What Mastery Looks Like: A student accurately adds, subtracts, multiplies, and divides complex numbers, leaving answers in a + bi form. The student can plot a complex number and explain how conjugates produce a real denominator.
Common Misconceptions: Students may treat i² as 1 instead of -1 or combine real and imaginary terms as like terms. They may also distribute signs incorrectly or divide real and imaginary parts separately instead of using a conjugate.
How to Assess It: Exit ticket: Simplify ((3 + 2i)(1 - i)) / (1 + i) to a + bi, then plot the result on the complex plane.

Lesson moves

Use coordinate grid mats and complex-number cards; students place each card at (a, b), then add numbers by moving horizontally and vertically.
Ask students to write why multiplying the numerator and denominator by a conjugate removes i from the denominator.
Run a card sort matching expressions, intermediate steps, and standard form answers, including distractors based on i² = 1.
Have students combine series impedances of 4 + 3i ohms and 2 - 5i ohms, then interpret the real and imaginary parts.

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