A $90^\circ$ rotation in the clockwise direction corresponds to multiplication by $\operatorname{cis} (-90^\circ) = -i.$

[asy]
unitsize(0.4 cm);

pair O = (-4,-5), A = (3,0), B = rotate(-90,O)*(A);

draw(O--A,dashed);
draw(O--B,dashed);

dot("$3$", A, NE);
dot("$1 - 12i$", B, SE);
dot("$-4 - 5i$", O, W);
[/asy]

Let $z$ be the image of $3$ under the rotation.  Since center of the rotation is $-4 - 5i,$
\[z - (-4 - 5i) = (-i)(3 - (-4 - 5i)).\]Solving, we find $z = \boxed{1 - 12i}.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
A $90^\circ$ rotation around $-4 - 5i$ in the clockwise direction is applied to $3$ (as a complex number).  What is the resulting complex number?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
1 - 12i
A $90^\circ$ rotation around $-4 - 5i$ in the clockwise direction is applied to $3$ (as a complex number).  What is the resulting complex number?
test