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}