Question

If the complex number x = 3 + bi and |x|^2 = 13, which is a possible value of b?

Answer 1

If x=3+bi, then

$|x|=\sqrt{3^2+b^2}.$

You know that $|x|^2=13,$ then

$\left(\sqrt{3^2+b^2}\right)^2=13,\\ \\ 9+b^2=13,\\ \\b^2=4,\\ \\b=\pm 2.$

Two possible complex numbers satisfy these conditions:

$x_1=3+2i, \ x_2=3-2i.$

As you can see the possible value of b is 2.

Answer: correct choice is A.