AMC 12 2023 B Problem 12

For complex numbers u=a+b i and v=c+d i (where i=\sqrt{-1} ), define the binary operation

$$u \otimes v=a c+b d i$$

Suppose z is a complex number such that z \otimes z=z^{2}+40. What is |z|?

Answer Choices
A. 2
B. 5
C. \sqrt{5}
D. \sqrt{10}
E. 5 \sqrt{2}