Problem 2 Graphing in the Complex Number Plane
What are the graph and absolute value of each number?
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Think
Where is a pure imaginary number in the complex plane?
The real part of a pure imaginary number is 0. The number must be on the imaginary axis.
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6 i
✓ Got It?
- What are the graph and absolute value of each number?
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Essential Understanding You can define operations on the set of complex numbers so that when you restrict the operations to the subset of real numbers, you get the familiar operations on the real numbers.
To add or subtract complex numbers, combine the real parts and the imaginary parts separately. If the sum of two complex numbers is 0, or 0 + 0 i, then each number is the opposite, or additive inverse, of the other. The associative and commutative properties apply to complex numbers as well.
Problem 3 Adding and Subtracting Complex Numbers
What is each sum or difference?
Plan
How is adding complex numbers similar to adding algebraic expressions?
Adding the real parts and imaginary parts separately is like adding like terms.
✓ Got It?
- What is each sum or difference?
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Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions