Simplifying Radicals Review and Radicals as Exponents
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Simplifying Radicals Basic Review
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Simplifying Radicals Steps 1. Use a factor tree to put the
number in terms of its prime factors. 2. Group the same factor in
groups of the number on the outside. 3. Merge those numbers into 1
and place on the outside. 4. Multiply the numbers outside together
and the ones left on the inside together.
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Simplifying Radicals Adding and Subtracting
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Square Roots as Exponents Square RootExponent
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Bellringer 9/24/14
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Exponent Rules and Imaginary Numbers - with multiplying and
dividing square roots if we have time
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Imaginary Numbers
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Exponent Rules Zero Exponent Property A base raised to the
power of 0 is equal to 1. a 0 = 1 Negative Exponent Property
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Exponent Rules Product of Powers Property Quotient of Powers
Property
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Exponent Rules Power of a Power Property Power of a Product
Property
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Exponent Rules Power of a Quotient Property
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Bellringer 9/25/14
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Imaginary Numbers and Exponents
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MultiplicationDivision b may not be equal to 0. The Rules
(Properties) Roots and Radicals Review
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MultiplicationDivision b may not be equal to 0. The Rules
(Properties) Roots and Radicals
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MultiplicationDivision Examples: Roots and Radicals Review
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MultiplicationDivision Examples: Roots and Radicals Review
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To add or subtract square roots or cube roots... simplify each
radical add or subtract LIKE radicals by adding their coefficients.
Two radicals are LIKE if they have the same expression under the
radical symbol. Intermediate Algebra MTH04 Roots and Radicals
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Complex Numbers
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All complex numbers are of the form a + bi, where a and b are
real numbers and i is the imaginary unit. The number a is the real
part and bi is the imaginary part. Expressions containing imaginary
numbers can also be simplified. It is customary to put I in front
of a radical if it is part of the solution.
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Simplifying with Complex Numbers Practice
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Bellringer 9/26/14 1. Sub Rules Apply
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Practice With Sub simplify, i, complex, exponent rules
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Bellringer 9/29/14 Write all of these questions and your
response 1. Is this your classroom? 2. Should you respect other
peoples property and work space? 3. Should you alter Mrs.
Richardsons Calendar? 4. How should you treat the class set of
calculators?
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Review Practice Answers Discuss what to do when there is a
substitute
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Bellringer 9/30/14 *EQ- What are complex numbers? How can I
distinguish between the real and imaginary parts? 1. 1. How often
should we staple our papers together? 2. When should we turn in
homework and where? 3. When and where should we turn in late work?
4. What are real numbers?
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Lets Review the real number system! Rational numbers Integers
Whole Numbers Natural Numbers Irrational Numbers
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More Examples of The Real Number System
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Now we have a new number! Complex Numbers Defined. Complex
numbers are usually written in the form a+b i, where a and b are
real numbers and i is defined as. Because does not exist in the set
of real numbers I is referred to as the imaginary unit. If the real
part, a, is zero, then the complex number a +b i is just bi, so it
is imaginary. 0 + b i = b i, so it is imaginary If the real part,
b, is zero then the complex number a+b i is just a, so it is real.
a+ 0 i = a, so it is real
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Examples Name the real part of the complex number 9 + 16 i?
What is the imaginary part of the complex numbers 23 - 6 i?
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Check for understanding Name the real part of the complex
number 12+ 5 i? What is the imaginary part of the complex numbers
51 - 2 i? Name the real part of the complex number 16 i? What is
the imaginary part of the complex numbers 23 ?
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Name the real part and the imaginary part of each. 1. 2. 3. 4.
5.
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Bellringer 10/1/14 *EQ- How can I simplify the square root of a
negative number? For Questions 1 & 2, Name the real part and
the imaginary part of each. 1. 2. For Questions 3 & 4, Simplify
each of the following square roots. 3. 4.
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Simply the following Square Roots.. 1. 2. 3. 4. How would you
take the square root of a negative number??
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Simplifying the square roots with negative numbers The square
root of a negative number is an imaginary number. You know that i =
When n is some natural number (1,2,3,), then
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Simply the following Negative Square Roots.. 1. 2. 3.
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Lets review the properties of exponents.
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How could we make a list of i values?
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Practice Simply the following Negative Square Roots.. 1. 2. 3.
Find the following i values.. 4. 5.
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Bellringer 10/2/14
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How could we make a list of i values?
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Note: A negative number raised to an even power will always be
positive A negative number raised to an odd power will always be
negative.
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How could we make a list of i values?
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Bellringer 10/3/14 Turn in your Bellringers
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Bellringer 10/13/14
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Review
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Review Work on your own paper
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Bellringer 10/14/14
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Review/practice Complex Numbers
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Bellringer 10/16/14
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Bellringer 10/17/14
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Bellringer 10/20/14(7th)
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Bellringer 10/20/14
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Remember 28
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Answer: -i
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Conjugate of Complex Numbers
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Conjugates In order to simplify a fractional complex number,
use a conjugate. What is a conjugate?
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are said to be conjugates of each other.
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Lets do an example: Rationalize using the conjugate Next
