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# Complex Numbers and Difference Equations



**Learning Objectives**:

<!-- This chapter lays the basics for learning multi-step methods for solving ordinary differential equations.  -->
After completing this chapter you should be able to:
- Simplify algebraic expressions for complex variables and find the corresponding real and imaginary components;
- Understand the definition of difference equation;
- Distinguish different types of difference equations, telling their
  * Order,
  * Linearity (linear or nonlinear),
  * Homogeneity (homogeneous or non-homogeneous);      
- Find the general solution to a homogeneous linear difference equation. 


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