# Complex numbers

## 10.1 Introduction

In the previous chapter, we have shown that a single frequency wave can be represented by a phasor. We begin this chapter with a brief look at linear system theory. Such systems, when the input is a single frequency wave, produce an output at the same frequency which may be phase shifted with a scaled amplitude. Using complex numbers the system can be represented by a number which multiplies the input phasor having the effect of rotating the phasor and scaling the amplitude. We can define j as the number which rotates the phasor by π /2 without changing the amplitude. If this multiplication is repeated, hence rotating the phasor by (π/2) + (π /2) = π, then the system output will be inverted. In this way we can ...

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