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Radicals and Complex Numbers N-CN.1 Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real. N-CN.2 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Simplifying Radicals • The number underneath the radical symbol is called the radicand • To simplify: • Write out all of the prime factors of the radicand • Remove numbers from the radical based on the root • If there is a number in front of the radical (coefficient) MULTIPLY that number by the number(s) that are removed from the radical Simplifying Radicals • For square root: Take out pairs of the same number EX: 294 EX: −5 392 • For cube root: Take out groups of three of the same number 3 EX: 128 3 EX: −2 648 • For 4th root and above: Take out groups of four of the same number, etc. 4 EX: 48 6 EX: −7 384 Simplifying Negative Radicals (Imaginary Numbers) 𝒊 = −𝟏 • If the radicand is a negative number, simplify the same except i has to be moved to the front of the radical EX: 3 −49 EX: −600 EX: −4 −18 Complex Numbers • A number that is written in the form: 𝑎 + 𝑏𝑖 • In calculator: Use 2nd . to type in i EX: (−5𝑖)– (−3– 3𝑖) EX: (−6𝑖)(−5𝑖) 3−2𝑖 4𝑖 EX: (4 + 3𝑖)(−1– 7𝑖) EX: EX: (5 + 4𝑖)2 EX: 6 + 𝑖 + (−1 − 4𝑖)