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## 3.3. Complex numbers

Complex numbers are used in engineering, science, and other technology applications, especially, in control engineering.
Definition of complex number
A complex number is a number that can be written in standard form as a + bi, where a and b are real numbers and i is an imaginary unit $(i=−1)$.
We call a the real part of the complex number and bi the imaginary part of the complex number. The imaginary unit (number) i is sometimes denoted by j.
For a complex number, z has the rectangular form as z = x + yi, where x and y are real numbers,

$x=Rez(realpartofz),y=Imz(imaginarypartofz)$

For example, the following are complex numbers:

$0+0i=$

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