Montana Math MT.PLUS.NUM.REAS.2.b
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: Finding the conjugate of a complex number.
2026 Montana Mathematics Content Standards · Number and Quantity
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students write complex numbers in the form a + bi and identify the real and imaginary parts. They use i² = −1 and find a conjugate by changing only the sign of the imaginary part.
What Mastery Looks Like
- Given −4 + 6i, a student writes −4 − 6i without changing the real part. They recognize that 5 is its own conjugate because its imaginary part is zero.
Common Misconceptions
- Students may change both signs, turning −2 + 3i into 2 − 3i. They may think 7 has no conjugate instead of writing it as 7 + 0i.
How to Assess It
- Exit ticket: Find the conjugates of −2 + 5i, 4 − i, and 7. Write 7 in a + bi form first.
Lesson moves
Ways to Teach It
Give pairs two-color counters and a mat labeled real and imaginary; build 3 + 2i, then flip only the imaginary counters.
Ask students to write why the conjugate of −2 − 5i is −2 + 5i, not 2 + 5i.
Play a matching game with cards showing 4 + i, 4 − i, −3 + 2i, and −3 − 2i.
Show a circuit card marked 4 + 3i ohms; ask students to choose its conjugate from 4 − 3i and −4 − 3i.
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Related Standards
- 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, mul...
- MT.PLUS.NUM.REAS.2.a
Adding, subtracting, multiplying, and dividing complex numbers, and
- MT.PLUS.ALG.POLY.4
Solve quadratic equations that have complex solutions and understand why the solutions form a conjugate pair.
- MT.PLUS.ALG.FUN.2
Understand the relationship between a function and its inverse.
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