if the complex number x = 3 + bi and |x|² = 13, which is a possible value of b?\n2\n4\n9\n10

Explanation:

Step1: Recall modulus formula for complex number

For a complex number $x = a+bi$, $|x|=\sqrt{a^{2}+b^{2}}$, so $|x|^{2}=a^{2}+b^{2}$. Here $a = 3$.

Step2: Substitute values into the formula

We have $|x|^{2}=3^{2}+b^{2}$. Since $|x|^{2}=13$, then $3^{2}+b^{2}=13$.

Step3: Solve for $b$

$9 + b^{2}=13$, so $b^{2}=13 - 9=4$. Then $b=\pm2$.

Answer:

A. 2