Download Imaginary Numbers i

Objective: You will write, add,
subtract, multiply, and divide
complex numbers.
The Standard Form
a  bi
- where a and b are real numbers
a = the real part of the complex number
bi = the imaginary part of the complex number
b = the coefficient of the imaginary number
Complex Numbers
Real Numbers
Imaginary Numbers
i 
1
1
• Every real number is a complex number
because a = a + 0i .
• Every imaginary number is a complex number
because bi = 0 + bi .
Imaginary Numbers
Why do we have imaginary numbers?
Imaginary numbers were invented so that
negative numbers would have square roots
and certain equations would have solutions.
For instance, an equation like x2 = -1 has no
real solution because you cannot take the
square root of -1.
i  1
sadi =
-1
Imaginary Numbers
i=i
i5 = i
i2 = -1
i6 = -1
i3 = -i
i7 = -i
i4 = 1
i8 = 1
Write in standard form:
5  27
16
5
3
18
Write in standard form:
5  27
16
5
0  4i
5  0i
5
3
5  3i 3
18
3  3i 2
Adding & Subtracting
Complex Numbers:
1. Combine like terms (treat the
“i” like a variable).
2. Write the answer in the form
a + bi or a – bi.

Examples:
1. (3 - i) + (2 + 3i)
2. 3 - (-2 + 3i) + (-5 + i)
3. 2i – (4 – 3i)
4. -2 + -8 + 5 - -50

 

Examples:
1. (3 - i) + (2 + 3i)  5  2i
2. 3 - (-2 + 3i) + (-5 + i)  0  2i
3. 2i – (4 – 3i)  4  5i
4. -2 + -8 + 5 - -50  3  3i 2

 

Multiplying & Dividing
Complex Numbers:
1. Multiplying Complex Numbers
A. Distribute, Box or FOIL.
B. Combine like terms.
C. Write as a + bi or a – bi
D. Replace all i2s with -1.
2. Divide Complex Numbers:
A. Multiply fraction (both top and bottom)
by the denominator’s conjugate.
B. Combine like terms.
C. Write as a + bi or a – bi.
Examples:
4 2  3i 
2  i 4  3i 
Examples:
4 2  3i   8  12i
2  i 4  3i 
 11 2i
Examples (continued):
5  2i
1 i
2  3i
4  2i
Examples (continued):
3 7
5  2i
  i
2 2
1 i
2  3i
1 4
  i
4  2i 10 5