This document provides an overview of complex numbers including: real numbers, imaginary numbers, and irrational numbers. It defines i as the square root of -1 and shows how to perform basic operations like addition, subtraction, multiplication, and division with complex numbers. The document also includes 5 examples of solving quadratics and operating with complex numbers, and assigns homework problems from page 277 involving working with complex numbers.

1. Algebra 2
5.4 Complex Numbers
Complex Numbers
Real Numbers Imaginary Numbers
A solution to a quadratic may be an _________________________________, such as 3i.
i = ___________. (By definition).
• Treat i like a variable.
What is i2
? ____________________
What is i3
? ____________________
What is i4
? ____________________
√– 5 is written __________________________.
SOLVING A QUADRATIC
EX 1: Solve 3x2
+ 10 = – 36
Rational Numbers
Integers
Natural
Numbers
Irrational Numbers

2. EX 2: Solve 2x2
+ 26 = – 10
EX 3: ADDING/SUBTRACTING COMPLEX NUMBERS
Write as a complex number in standard form (a + bi).
a. (4 – i) + (3 + 2i) b. (7 – 5i) – (1 – 5i) c. 6 – (– 2 + 9i) + (– 8 + 4i)
EX 4: MULTIPLYING COMPLEX NUMBERS
a. 5i(– 2 + i) b. (7 – 4i)(– 1 + 2i) c. (6 + 3i)(6 – 3i)
EX 5: DIVIDING COMPLEX NUMBERS
5 + 3i .
1 – 2i
HW p. 277 (18 – 26, 38 – 62 even)