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(B) Let $z = x + iy$. Given $|z| + z = 3 + i$. Substituting $z = x + iy$,we get $\sqrt{x^2 + y^2} + x + iy = 3 + i$. Comparing the imaginary parts,we

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$\frac{5}{3}$

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(B) Let $z = x + iy$. Given $|z| + z = 3 + i$. Substituting $z = x + iy$,we get $\sqrt{x^2 + y^2} + x + iy = 3 + i$. Comparing the imaginary parts,we get $y = 1$. Comparing the real parts,we get $\sqrt{x^2 + 1} + x = 3$. $\sqrt{x^2 + 1} = 3 - x$. Squaring both sides,$x^2 + 1 = (3 - x)^2 = 9 - 6x + x^2$. $1 = 9 - 6x$,which implies $6x = 8$,so $x = \frac{4}{3}$. Now,$|z| = \sqrt{x^2 + y^2} = \sqrt{(\frac{4}{3})^2 + 1^2} = \sqrt{\frac{16}{9} + 1} = \sqrt{\frac{25}{9}} = \frac{5}{3}$.

Let $z$ be a complex number such that $|z| + z = 3 + i$ (where $i = \sqrt{-1}$). Then $|z|$ is equal to

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