Download 1.1 Writing Complex Numbers

Warm Up for 1.1 in Math 2
Solve the equation.
3
1. Simplify
ANSWER
4 –
3. 2(x + 7)2 = 16
5
12 + 3 5
11
–7 + 2 2 , –7 – 2
Solve the equation.
ANSWER
2. 3x2 + 8 = 23
4. Three times the square of
a number is 15. What is the
number?
ANSWER
5 , –
5
ANSWER
–
5 ,
5
2
1.1 Writing Complex
Numbers
Purple Math 2 Book
Solve
2
x
+4=0
• x2 = -4
• x = √(-4)
• In the real number system, there isn’t a number we
can square to get -4.
• Imaginary numbers: Don’t think of them as “not
real”
• Mathematicians chose this term for the square root
of a negative number after they thought all real
numbers were identified-(thought no real life
application)
Imaginary Numbers
i  1
i  i  i  1
2
The square root of
negative numbers
Examples:
3
4 
12 
If i  -1, then
1  i
2
i  1
*For larger exponents,
divide the exponent by
4, then use the
remainder as your
exponent instead.
Example:
etc.
i
23
?
Complex Numbers
• A complex number has a real part & an
imaginary part.
• Standard form is:
a  bi
Real part
Example: 5+4i
Imaginary part
i
• Anytime you have √-1, you replace it with i
•
•
•
•
√-16
√16 * √-1
4 * i
4i
How do we write the square root of a
negative number?
• √-1 is called i or an imaginary unit—it is a way
to describe the square root of a negative number
• (√-1 )2
• √-1 * √-1
• Therefore, i2 = -1.
• i = √-1
i2 = -1
• i3 = (√-1 )3 = -i
• i4 = (√-1 )4= -1*-1 = 1
Write the complex number in
standard form.
1. √-1
2. √-25
i
3. √-8
5i
4. √-32
2i √2
4i √2
Complex Numbers (a + bi)
real (a) + imaginary (bi)
Real
Numbers
Just a
(a + 0i)
-1
½
pi
√3
Imaginary Numbers
(a + bi, b ≠ 0)
2 + 3i
5-5i
Pure Imaginary Numbers
(0 + bi, b ≠ 0, no a)
-4i
5i
Write the complex number in
standard form.
5. 2 - √-9
2 -3i
6. 7 - √-27
7-3i√3
With a partner, do p. 3 in M2
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