The student will perform operations on complex numbers and express the results in simplest form using patterns of the powers of i.
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A complex number multiplied by its conjugate is a real number.
Equations having no real number solutions may have solutions in the set of complex numbers.
Algebraic properties apply to complex numbers as well as real numbers.
All complex numbers can be written in the form 𝑎 + 𝑏𝑖 where 𝑎 and 𝑏 are real numbers and 𝑖 is the imaginary unit that satisfies the equation 𝑖² = −1 (e.g., 3 + 2𝑖; ±√−9 = 0 ± 3𝑖; 5 = 5 + 0𝑖).
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to