College Algebra: Section 1.4 (Packet #8)
By the end of the section, you should be able to:
- Classify a complex number by its real and imaginary parts.
- Add, Subtract, Multiply and Divide complex numbers.
- Determine whether real number properties hold with complex numbers.
Definitions:
Overview of Complex Numbers and the Imaginary Unit:
🎥Explained
🎥Explained
Algebra of Complex Expressions
Algebra of Complex Expression Examples
🎥Examples 1,2,&3 🎥Example 4
🎥Examples 1,2,&3 🎥Example 4
Things to remember about the Algebra of Complex Expressions:
- For Addition/Subtraction: collect and combine like parts (real/imaginary).
- For Multiplication: FOIL (First, Outer, Inner, Last) this is really the distributive property.
- Remember i*i = i2 = -1
- For Division: “real”ize the denominator by multiplying the denominator by its complex conjugate.
Simplifying Radical Expressions with COMPLEX NUMBERS
Remember that our properties for simplifying radical expressions such as:
Remember that our properties for simplifying radical expressions such as:
are defined only when a and b are REAL numbers. If a and/or b is not true, these properties do not necessarily hold.
For example:
For example:
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