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## Complex Numbers

### Creating Complex Numbers

Complex numbers consist of two separate parts: a real part and an imaginary part. The basic imaginary unit is equal to the square root of -1. This is represented in MATLAB® by either of two letters: i or j.

The following statement shows one way of creating a complex value in MATLAB. The variable x is assigned a complex number with a real part of 2 and an imaginary part of 3:

```x = 2 + 3i;
```

Another way to create a complex number is using the complex function. This function combines two numeric inputs into a complex output, making the first input real and the second imaginary:

```x = rand(3) * 5;
y = rand(3) * -8;

z = complex(x, y)
z =
4.7842 -1.0921i   0.8648 -1.5931i   1.2616 -2.2753i
2.6130 -0.0941i   4.8987 -2.3898i   4.3787 -3.7538i
4.4007 -7.1512i   1.3572 -5.2915i   3.6865 -0.5182i
```

You can separate a complex number into its real and imaginary parts using the real and imag functions:

```zr = real(z)
zr =
4.7842    0.8648    1.2616
2.6130    4.8987    4.3787
4.4007    1.3572    3.6865

zi = imag(z)
zi =
-1.0921   -1.5931   -2.2753
-0.0941   -2.3898   -3.7538
-7.1512   -5.2915   -0.5182
```

### Complex Number Functions

See Complex Number Functions for a list of functions most commonly used with MATLAB complex numbers in MATLAB.

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