Montana Math MT.PLUS.NUM.REAS.2

MT.PLUS.NUM.REAS.2 is a cluster heading. These are the individual standards under it.

• MT.PLUS.NUM.REAS.2.a

  Adding, subtracting, multiplying, and dividing complex numbers, and

• MT.PLUS.NUM.REAS.2.b

  Finding the conjugate of a complex number.

01

What Students Need to Do

Students write complex numbers in the form a+bi and use i²=−1 to calculate with them. They add, subtract, multiply, and divide complex numbers, and find their conjugates.

02

What Mastery Looks Like

A student simplifies (2+i)(1−i) to 3−i and names 2−i as the conjugate of 2+i. When dividing, they multiply the top and bottom by the denominator's conjugate and give the answer in a+bi form.

03

Common Misconceptions

Students may leave i² in an answer instead of replacing it with −1. They may change both signs when finding a conjugate, or multiply only the denominator by the conjugate when dividing.

04

How to Assess It

Exit ticket: Let z=3+2i and w=1−i. Find z+w, z−w, zw, z/w, and the conjugate of w; show how you made the division denominator real.

1. 01

   Give pairs paper cards marked 1, −1, i, and −i; have them build (2+i)+(1−2i) and cancel opposites.

2. 02

   Ask, 'Why does (3+2i)(3−2i) have no i term?' Have students write the line that shows the cancellation.

3. 03

   Put (2+i)/(1−i), (2+i)(1−i), and (2+i)−(1−i) on cards; students match each expression to its simplified answer.

4. 04

   On a map grid, mark a robot at 3+2i and its conjugate at 3−2i; describe the reflection across the east-west axis.

• MT.PLUS.ALG.POLY.4

  Solve quadratic equations that have complex solutions and understand why the solutions form a conjugate pair.

• MT.6.NS.6

  Understand a rational number as a point on the number line and extend number line diagrams and coordinate axes by: Recognizing opposite signs of numbers as indi...