1.1 Write Complex Numbers. Vocabulary A number r is a square root of a number s if r 2 = s. The...
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Transcript of 1.1 Write Complex Numbers. Vocabulary A number r is a square root of a number s if r 2 = s. The...
![Page 1: 1.1 Write Complex Numbers. Vocabulary A number r is a square root of a number s if r 2 = s. The expression is called a radical. –The symbol is a radical.](https://reader036.fdocuments.us/reader036/viewer/2022082819/56649e025503460f94aec19b/html5/thumbnails/1.jpg)
1.1 Write Complex Numbers
![Page 2: 1.1 Write Complex Numbers. Vocabulary A number r is a square root of a number s if r 2 = s. The expression is called a radical. –The symbol is a radical.](https://reader036.fdocuments.us/reader036/viewer/2022082819/56649e025503460f94aec19b/html5/thumbnails/2.jpg)
Vocabulary
• A number r is a square root of a number s if r2 = s.
• The expression is called a radical.
– The symbol is a radical sign and the number s beneath the radical sign is the radicand of the expression.
s
![Page 3: 1.1 Write Complex Numbers. Vocabulary A number r is a square root of a number s if r 2 = s. The expression is called a radical. –The symbol is a radical.](https://reader036.fdocuments.us/reader036/viewer/2022082819/56649e025503460f94aec19b/html5/thumbnails/3.jpg)
Vocabulary
• Product Property of Radicals
• Quotient Property of Radicals
ab a b a a
b b
![Page 4: 1.1 Write Complex Numbers. Vocabulary A number r is a square root of a number s if r 2 = s. The expression is called a radical. –The symbol is a radical.](https://reader036.fdocuments.us/reader036/viewer/2022082819/56649e025503460f94aec19b/html5/thumbnails/4.jpg)
Vocabulary
• The imaginary unit i is defined as
2
-1
-1
i
where
i
![Page 5: 1.1 Write Complex Numbers. Vocabulary A number r is a square root of a number s if r 2 = s. The expression is called a radical. –The symbol is a radical.](https://reader036.fdocuments.us/reader036/viewer/2022082819/56649e025503460f94aec19b/html5/thumbnails/5.jpg)
Vocabulary
• A complex number written in standard form is a number a + bi where a and b are real numbers. – The number a is the real part of the complex
number, and the b number is the imaginary part.
– Example: 2 + 3i
Real Part
Imaginary Part
![Page 6: 1.1 Write Complex Numbers. Vocabulary A number r is a square root of a number s if r 2 = s. The expression is called a radical. –The symbol is a radical.](https://reader036.fdocuments.us/reader036/viewer/2022082819/56649e025503460f94aec19b/html5/thumbnails/6.jpg)
Vocabulary
• If b = 0, then a + bi is an imaginary number.
• If a = 0 and b = 0, then a + bi is a pure imaginary number. – 0 + bi = bi
(there is not an real part…NO “a”)
![Page 7: 1.1 Write Complex Numbers. Vocabulary A number r is a square root of a number s if r 2 = s. The expression is called a radical. –The symbol is a radical.](https://reader036.fdocuments.us/reader036/viewer/2022082819/56649e025503460f94aec19b/html5/thumbnails/7.jpg)
Vocabulary
• Two complex numbers a + bi and c + di are equal if and only if a = c and b = d.
• For example, if x + yi = 5 – 3i, then x = 5 and y = -3
![Page 8: 1.1 Write Complex Numbers. Vocabulary A number r is a square root of a number s if r 2 = s. The expression is called a radical. –The symbol is a radical.](https://reader036.fdocuments.us/reader036/viewer/2022082819/56649e025503460f94aec19b/html5/thumbnails/8.jpg)
Example 1:
• Simplify the expression
a)
b)
8 6
5
36
![Page 9: 1.1 Write Complex Numbers. Vocabulary A number r is a square root of a number s if r 2 = s. The expression is called a radical. –The symbol is a radical.](https://reader036.fdocuments.us/reader036/viewer/2022082819/56649e025503460f94aec19b/html5/thumbnails/9.jpg)
Example 2:
• Write complex numbers in standard forma)
b)
c)
d)
25
3
12
4 16
![Page 10: 1.1 Write Complex Numbers. Vocabulary A number r is a square root of a number s if r 2 = s. The expression is called a radical. –The symbol is a radical.](https://reader036.fdocuments.us/reader036/viewer/2022082819/56649e025503460f94aec19b/html5/thumbnails/10.jpg)
Example 3:
• Find real numbers x and y to make the equation true.
1) 4x – 4yi = 8 – 12i
2) 5x + 3yi = 10 + 18i
![Page 11: 1.1 Write Complex Numbers. Vocabulary A number r is a square root of a number s if r 2 = s. The expression is called a radical. –The symbol is a radical.](https://reader036.fdocuments.us/reader036/viewer/2022082819/56649e025503460f94aec19b/html5/thumbnails/11.jpg)
Classwork
• Out of your notetaking guide
pg. 4 – 5 ALL