# Documentation

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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 ```