CN.7 vs REI.4b

[dhh]

Help me to see the difference.

REI.4b (last part)
Cluster: Solve quadratic equations in one variable.
Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

This seems to tell me that they need to understand the discriminant and then write the solution as a complex number.

CN.7
Solve quadratic equations with real coefficients that have complex solutions.

This seems to tell me that they are solving quadratic equations and then writing the solutions as complex numbers.

It seems to me that REI.4b completely encompasses CN.7. What am I missing?

Thanks,
Dave

[Bill McCallum]

This is a case where coherence trumped conciseness in writing the standards. The skill and the piece of knowledge named by these two standards are the same, but the context is different. In A-REI.4b the context is solving equations, and you want students to know that sometimes solving equations leads to complex numbers. In CN.7 the context is the complex numbers as a system, and you want students to know that they can sometimes provide solutions to equations that didn’t have solutions before. These are two different understandings, two different ways of viewing the same piece of knowledge, and approaching that piece of knowledge from both sides seemed worthwhile.

[Author]

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