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9.1 complex numbers 2016 ink.notebook
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ch 7
Exponents
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Unit 9 Radicals
9.1
Complex
Numbers
1
9.1 complex numbers 2016 ink.notebook
February 21, 2017
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Lesson Objectives
Standards
Lesson Notes
9.1 Complex Numbers
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Lesson Objectives
Standards
Lesson Notes
Lesson Objectives
A.SSE.2
Standards
Lesson Notes
I will rewrite a complex expression in simplest form A.SSE.2. Use the structure of an expression to identify ways to rewrite it.
N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
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9.1 complex numbers 2016 ink.notebook
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Not all radicals have real number solutions. Mathematicians created an expanded
number system using the imaginary unit i. The imaginary unit i can be used to write the square root of any negative number and is defined
It follows then A complex number written in standard form is the number
a + bi where a is the real number part and bi is the
imaginary part.
Identify real number parts and imaginary number parts.
1. 7 + 3i 2. 8 – i
3. 5i
4. 2
3
9.1 complex numbers 2016 ink.notebook
Complex Numbers
(imaginary numbers)
i
i
=
2
-1
= -1
February 21, 2017
A negative on the inside
Pulls an i to the outside
-4 = 2i
- -16 = -4i
-5 =
2
i
5
(3i ) = 32 i
9 -1 = -9
2
Examples. Solve each: 5.
6.
7.
8.
9.
10.
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9.1 complex numbers 2016 ink.notebook
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Examples. Solve each: 11.
12.
13.
14.
15.
16.
Parts of a Radical
radical symbol
index
36
radicand
Converting between Radical Form and
Rational Exponent Form
i
x
e
e
=xi
exponent over index
1
radical
If the index is not written,
it is automatically a 2.
2
1
81 = 2 81 = 81
3
4
3
4
81 = 81
5
9.1 complex numbers 2016 ink.notebook
February 21, 2017
21.
22.
Write each expression in radical form.
17.
18.
23.
19.
24.
20.
25.
27.
26.
28.
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9.1 complex numbers 2016 ink.notebook
29.
30.
31.
32.
On Your
Whiteboards
February 21, 2017
Solve each:
a)
b)
c)
d)
e)
f)
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9.1 complex numbers 2016 ink.notebook
On the
Worksheet
February 21, 2017
Homework
Solve. 1.
3.
2.
4.
5.
7.
6.
8.
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9.1 complex numbers 2016 ink.notebook
9.
10.
February 21, 2017
Identify real number parts and imaginary number parts.
13. 3 + 2i 11.
12.
Write each expression in radical form.
17.
18.
19.
20.
14. 9 – 3i
15. 4i
16. 6
Write each expression in radical form.
21.
22.
23.
24.
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9.1 complex numbers 2016 ink.notebook
Write each expression in radical form.
25.
26.
February 21, 2017
Write each radical in exponential form.
29.
31.
27.
35.
32.
28.
Write each radical in exponential form.
33.
30.
34.
35.
Write each radical in exponential form.
37.
39.
38.
40.
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9.1 complex numbers 2016 ink.notebook
41.
45.
42.
46.
.
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43.
44.
47.
48.
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9.1 complex numbers 2016 ink.notebook
February 21, 2017
Answers:
12