MA19.A1.3

Mathematics (2019) Grade(s): 09-12 - Algebra I with Probability

MA19.A1.3
Define the imaginary number i such that $i^2 = -1$.

Unpacked Content

Knowledge

Students know:

Which manipulations of radicals produce equivalent forms.
The extension of the real numbers which allows equations such as x² = -1 to have solutions is known as the complex numbers and the defining feature of the complex numbers is a number i, such that i² = -1.

Skills

Students are able to:

Perform manipulations of radicals, including those involving square roots of negative numbers, to produce a variety of forms, for example, √(-8) = i√(8) = 2ⁱ√(2).

Understanding

Students understand that:

When quadratic equations do not have real solutions, the number system must be extended so that solutions exist. and the extension must maintain properties of arithmetic in the real numbers.

Vocabulary

Complex number

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