CCSS.Math.Content.HSN-CN.A

CCSS.Math.Content.HSN-CN.A is a cluster heading. These are the individual standards under it.

• CCSS.Math.Content.HSN-CN.A.1

  Know there is a complex number i such that i² = -1, and every complex number has the form a + bi with a and b real.

• CCSS.Math.Content.HSN-CN.A.2

  Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

• CCSS.Math.Content.HSN-CN.A.3

  (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

01

What Students Need to Do

Students write complex numbers in a + bi form and calculate sums, differences, and products. They use i² = -1 to simplify powers and products. They use conjugates to simplify quotients and find modulus.

02

What Mastery Looks Like

Students correctly add, subtract, and multiply complex numbers, then write answers in a + bi form. They simplify powers of i and use conjugates to find quotients or moduli. Their work keeps real and imaginary parts clearly separated.

03

Common Misconceptions

Students may treat i as a variable instead of using i² = -1. They may combine real and imaginary parts incorrectly or forget to simplify powers of i. When dividing, some multiply only one term by the conjugate.

04

How to Assess It

Give this exit ticket: simplify (3 + 2i)(1 - 4i), then explain where i² = -1 was used. Ask students to write the answer in a + bi form.

1. 01

   Use graph paper and arrow cutouts to model adding 3 + 2i and -1 + 4i on the complex plane.

2. 02

   Ask students to explain why i² = -1 changes the product (2 + 3i)(2 - 3i) into a real number.

3. 03

   Play a matching game with cards showing complex expressions, simplified answers, powers of i, and equivalent conjugate forms.

4. 04

   Give resistor and reactance values, then have students write and add complex impedances for a simple series circuit.

• CCSS.Math.Content.HSA-APR.A

  Perform arithmetic operations on polynomials

• CCSS.Math.Content.HSN-CN.C

  Use complex numbers in polynomial identities and equations.

• CCSS.Math.Content.HSN-CN.B

  Represent complex numbers and their operations on the complex plane.

• CCSS.Math.Content.HSN-CN.B.5

  (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representatio...