Florida B.E.S.T. MA.912.NSO.2.1

MathGrades 9–12Represent and perform operations with expressions within the complex number system.

The Standard

Extend previous understanding of the real number system to include the complex number system. Add, subtract, multiply and divide complex numbers.

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

Teacher's field guide

What Students Need to Do: Students identify real and imaginary parts and use i²=-1 to simplify expressions. They add, subtract, multiply, and divide complex numbers, writing answers in a+bi form.
What Mastery Looks Like: Students accurately combine like terms, distribute factors, and replace i² with -1. They use conjugates when dividing and write final answers in a+bi form.
Common Misconceptions: Students may combine real and imaginary terms as if they were like terms. They may treat i² as 1, distribute signs incorrectly, or divide without using the complex conjugate.
How to Assess It: Use a four-item exit ticket: simplify (3+2i)+(4-5i), (6+i)-(2-3i), (2+i)(3-2i), and (4+2i)/(1-i).

Lesson moves

Give pairs red cards for real terms and blue cards for imaginary terms, then have them model and simplify sums and differences.
Ask students to write why multiplying a complex denominator by its conjugate produces a real number.
Set up answer-matching cards where students simplify complex number expressions and find the card showing each correct result.
Give an AC circuit impedance and voltage, then have students divide the complex numbers to find the circuit's current.

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