exam study radical expressions and complex numbers
TRANSCRIPT
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Exam Study
Radical Expressions and Complex Numbers
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Closure of Sets Under the Four Basic Operations
• Real Numbers are closed under all operations.• Irrational Numbers are not closed under the
four basic operations. • Rational Numbers are closed under the four
basic operations. • Integers are closed on all except division.
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Radicals and Rational Exponents
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Simplifying Radicals and Rational Exponents
• Examples:
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Adding and Subtracting Radicals
1. Simplify all Radicals2. Identify radicals with the SAME INDEX and
SAME RADICAND. (only these can be combined)
3. For common radicals. Add/subtract the coefficients and KEEP THE COMMON RADICAL
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Example:
3√−40𝑎7+2𝑎2 3√135𝑎4
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Example
√98 𝑥4 𝑦 2−3 𝑥2 𝑦 √2
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Multiplying Radicals
1. Multiply the coefficients, then use the PRODUCT RULE:
2. SIMPLIFY the resulting radical
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Example
24√𝑝2𝑞 ∙7 4√𝑝3𝑞10
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Example
(√𝑥−√9 ) (√𝑥+9 )
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Steps to Divide Radicals
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Example:
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Example:
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plex Numbers
• and are REAL numbers.
• Each term has a name: = real part, = imaginary part
• When the complex number is simply a REAL number• When is an imaginary number• When , then that is called pure imaginary number
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Complex Numbers
I
Pure Imaginary Numbers
Imaginary NumbersReal Numbers
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What is the definition of a complex number?
a. A number of the form where and are real.
b. A number of the form where and is real.
c. A number of the form where is real and .
d. A number of the form where is real, and .
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Powers of Power Answer
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Adding and Subtracting Complex Numbers
(8+3 𝑖 )+(7+5 𝑖 )
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Adding and Subtracting Complex Numbers
(8+3 𝑖 )− (7−3 𝑖 )
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Multiplying Complex Numbers
(8+12 𝑖)(4−2𝑖)
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Identify: Real or Complex