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Radicals and Complex
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
• 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
EX: 128
EX: −2 648
• For 4th root and above: Take out groups of four of the same number,
EX: 48
EX: −7 384
Simplifying Negative Radicals (Imaginary
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)
EX: (4 + 3𝑖)(−1– 7𝑖)
EX: (5 + 4𝑖)2
EX: 6 + 𝑖 + (−1 − 4𝑖)