Montana Math MT.PLUS.NUM.REAS.2.a
The Standard
- MT.PLUS.NUM.REAS.2
- Understand there is a complex number i such that i² = −1, and every complex number has the form a + bi with a and b as real numbers by: Adding, subtracting, multiplying, and dividing complex numbers, and Finding the conjugate of a complex number.
Understand there is a complex number i such that i² = −1, and every complex number has the form a + bi with a and b as real numbers by: Adding, subtracting, multiplying, and dividing complex numbers, and
2026 Montana Mathematics Content Standards · Number and Quantity
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students add, subtract, multiply, and divide numbers with real and imaginary parts. They combine like terms, replace i² with -1, and use a conjugate when dividing.
What Mastery Looks Like
- Given 2+i and 1-i, a student can find all four results and write each with one real part and one imaginary part. They show their steps when multiplying and dividing.
Common Misconceptions
- Students may combine 2 and 3i as 5i or treat i² as 1. When dividing, they may multiply only the denominator by the conjugate or choose the wrong sign.
How to Assess It
- Exit ticket: Let z=2+i and w=1-i. Find z+w, z-w, zw, and z/w, and show your steps for multiplication and division.
Lesson moves
Ways to Teach It
Give pairs cards labeled 2, i, 3, and -i; have them arrange and calculate the four products in (2+i)(3-i).
Ask students to write two sentences explaining why (2+i)(2-i) has no imaginary part, then compare explanations with a partner.
Prepare four relay cards using 2+i and 1-i, one per operation; teams solve and check answers on the backs.
Give students an AC circuit card with voltage 3+4i volts and impedance 1+i ohms; ask them to divide to find current.
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