Let z be a complex number such that |z|+z=3+i | vedclass

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(D) Let $z = x + iy$,where $x, y \in \mathbb{R}$.Given $|z| + z = 3 + i$.Substituting $z = x + iy$,we get $\sqrt{x^2 + y^2} + x + iy = 3 + i$.Equating

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$\frac{5}{3}$

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(D) Let $z = x + iy$,where $x, y \in \mathbb{R}$.Given $|z| + z = 3 + i$.Substituting $z = x + iy$,we get $\sqrt{x^2 + y^2} + x + iy = 3 + i$.Equating the real and imaginary parts:$y = 1$ and $\sqrt{x^2 + y^2} + x = 3$.Substituting $y = 1$ into the second equation:$\sqrt{x^2 + 1} = 3 - x$.Squaring both sides:$x^2 + 1 = (3 - x)^2 = 9 - 6x + x^2$.$1 = 9 - 6x$ $\Rightarrow 6x = 8$ $\Rightarrow x = \frac{4}{3}$.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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