If x=3+bi, then
[tex]|x|=\sqrt{3^2+b^2}.[/tex]
You know that [tex]|x|^2=13,[/tex] then
[tex]\left(\sqrt{3^2+b^2}\right)^2=13,\\ \\ 9+b^2=13,\\ \\b^2=4,\\ \\b=\pm 2.[/tex]
Two possible complex numbers satisfy these conditions:
[tex]x_1=3+2i, \ x_2=3-2i.[/tex]
As you can see the possible value of b is 2.
Answer: correct choice is A.
