Download Lesson 1 - Coweta County Schools

• How do I use the
imaginary unit i to
write complex
numbers?
Write Complex Numbers
1.1
Properties of Radicals
a b
a b  _______
a
a

b __________
b __
Product property of radicals
Quotient property of radicals
Imaginary unit
i  1
i 
2

i  i
3

2
 1  1 i  1
4
i i
5
i  1
6
Write Complex Numbers
1.1
Example 1 Use properties of square roots
Simplify the expression.
a. 8  3  ___
2 6
4  _____
24  6  __
b.
3

49
3

7
___
49
___
3
__________
Product
________
property
Quotient
________
property
1.1
Write Complex Numbers
Checkpoint. Simplify the expression.
1. 150
5 2  3 5 5
5 6
150
15 10
5 35 2
Write Complex Numbers
1.1
Checkpoint. Simplify the expression.
18
2.
64
3 2 33

64
3 2

8
18

64
18
2
9
3 3
1.1
Write Complex Numbers
Example 2 Write complex numbers in standard form
a.
 16  16___
 1  16  __1  _____
4i
b.
 3  __
i 3
 1   __
3  __1  _____
3 ___
c. 9   25  ___
3  ___
25 ___
1
 __
 5i
 1  3_____
25  ___
3  ___
Write Complex Numbers
1.1
Checkpoint. Write the complex number in standard form.
3.
 144
144 1
144   1
12i
1.1
Write Complex Numbers
Checkpoint. Write the complex number in standard form.
4. 4   45
2  3 3  3  5  1
2  3i 5
45
5
9
3 3
1.1
Write Complex Numbers
Example 3 Equality of complex numbers
Find real numbers x and y to make the equation true.
a. 4 x  4 yi  8  12i
b. 5 x  3 yi  10  18i
Solution
a. ____
4x
___
x
 4y
_____
y
___
 ___
8
 ___
2

____
12
 ___
3
Set the ____
real parts equal to each other.
Divide each side by __
4 to solve for x.
Set the ___________
imaginary parts equal to
each other.
Divide each side by ___
 4to solve for y.
1.1
Write Complex Numbers
Example 3 Equality of complex numbers
Find real numbers x and y to make the equation true.
a. 4 x  4 yi  8  12i
b. 5 x  3 yi  10  18i
Solution
5x
b. ____
___
x
3y
_____
y
___
10
 ___
 ___
2
 ____
18
 ___
6
Set the ____
real parts equal to each
other.
Divide each side by __
5 to solve for x.
Set the ___________
imaginary parts equal to
each other.
Divide each side by __
3 to solve for y.
1.1
Write Complex Numbers
Checkpoint. Find real numbers x and y to make the
equation true.
5. 8 x  8 yi  16  24i
8x  16
x2
8 y  24
y3
6. 2 x  7 yi  14  21i
2x  14
x  7
 7 y  21
y  3
1.1
Write Complex Numbers
Pg. 4, 1.1 #1-32