Download Complex Numbers Notes

Algebra 2 / Trig
Name
Section 5.4 Complex Numbers
Block
Date
Review:
4  _______
because ____ * ____ = 4
9  _______
because ____ * ____ = 9
 9  _______
Imaginary Numbers
Imaginary number = _______________
Ex:
5 
i=
Ex:
Symbol = ___________
 49 
Ex:
12 
i2 =
Complex Numbers
Complex numbers = combine imaginary and real numbers
Ex. 5 + 3i
Adding and Subtracting
Add the corresponding numbers and imaginary coefficients
Examples:
1. (3 + 4i) + (5 – 3i) =
2. (2+ 3i) – (4 – 2i) =
3. (2 – 4i) – (-2 + 3i) =
Practice:
4. (5 + 6i) + (4 – 2i) =
5. (3+ 8i) – (12 – 10i) =
6. (1 – 11i) – (-4 + 9i) =
Multiplication
****When multiplying it is important to remember the powers of i****
Examples:
1. 5i(-2 + i ) =
2. (7 – 4i) (-1 + 2i) =
3. (6 + 3i) (6 – 3i) =
Practice:
4. 6i(-10 + 3i) =
5. (11 – 2i) (-5 + 7i) =
6. (5 + 4i) (8 – 10i) =
Division
In order to divide you need to multiply the numerator or denominator by the conjugate of the
denominator.
Examples:
5 3i
1.
1  2i
Practice:
5

3.
2i
5.
 5  3i

4i
2.
4  2i
3  3i
4.
3 i

3i
6.
10  i
2i
Homework: Page 277 #37, 39, 41, 47-60 First Column