Exam Study Radical Expressions and Complex Numbers.
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Transcript of Exam Study Radical Expressions and Complex Numbers.
Exam Study
Radical Expressions and Complex Numbers
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.
Radicals and Rational Exponents
Simplifying Radicals and Rational Exponents
• Examples:
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
Example:
3√−40𝑎7+2𝑎2 3√135𝑎4
Example
√98 𝑥4 𝑦 2−3 𝑥2 𝑦 √2
Multiplying Radicals
1. Multiply the coefficients, then use the PRODUCT RULE:
2. SIMPLIFY the resulting radical
Example
24√𝑝2𝑞 ∙7 4√𝑝3𝑞10
Example
(√𝑥−√9 ) (√𝑥+9 )
Steps to Divide Radicals
Example:
Example:
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
Complex Numbers
I
Pure Imaginary Numbers
Imaginary NumbersReal Numbers
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 .
Powers of Power Answer
Adding and Subtracting Complex Numbers
(8+3 𝑖 )+(7+5 𝑖 )
Adding and Subtracting Complex Numbers
(8+3 𝑖 )− (7−3 𝑖 )
Multiplying Complex Numbers
(8+12 𝑖)(4−2𝑖)
Identify: Real or Complex