[tex]\[

\begin{array}{c}

-2 - 3i \\

\text{and} \\

3 + 9i

\end{array}

\][/tex]

[tex]\[ d = \sqrt{(c - a)^2 + (d - b)^2} \][/tex]

Let's denote the given complex numbers as:

[tex]\[ z_1 = -2 - 3i \][/tex]

[tex]\[ z_2 = 3 + 9i \][/tex]

Here, [tex]\(a = -2\)[/tex], [tex]\(b = -3\)[/tex], [tex]\(c = 3\)[/tex], and [tex]\(d = 9\)[/tex]. Substitute these values into the distance formula:

[tex]\[ d = \sqrt{(3 - (-2))^2 + (9 - (-3))^2} \][/tex]

Simplify the terms inside the square root:

[tex]\[ c - a = 3 - (-2) = 3 + 2 = 5 \][/tex]

[tex]\[ d - b = 9 - (-3) = 9 + 3 = 12 \][/tex]

Now square these differences:

[tex]\[ (c - a)^2 = 5^2 = 25 \][/tex]

[tex]\[ (d - b)^2 = 12^2 = 144 \][/tex]

Then add these squared values:

[tex]\[ d = \sqrt{25 + 144} \][/tex]

[tex]\[ d = \sqrt{169} \][/tex]

Finally, take the square root of the sum:

[tex]\[ d = 13 \][/tex]

Therefore, the distance between the complex numbers [tex]\(-2 - 3i\)[/tex] and [tex]\(3 + 9i\)[/tex] is [tex]\(13.0\)[/tex].