Let z be a complex number such that left | vedclass

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Question

$z\, = \,x\, + \,iy$

$\sqrt {{x^2} + {y^2}} \, + \,x\, + \,iy\, = \,3\, + \,i$

$ \Rightarrow \,y = 1$

$\sqrt {{x^2} + 1} \, + \,x = 3 \Righta

Vedclass · Accepted Answer

$\frac{5}{3}$

Vedclass · Answer

$z\, = \,x\, + \,iy$

$\sqrt {{x^2} + {y^2}} \, + \,x\, + \,iy\, = \,3\, + \,i$

$ \Rightarrow \,y = 1$

$\sqrt {{x^2} + 1} \, + \,x = 3 \Rightarrow {x^2}\, + \,1 = 9 - 6x + {x^2}$

$ \Rightarrow \,x = \frac{4}{3}$

$|z|\, = \,\sqrt {{x^2}\, + \,{y^2}} \, = \,\frac{5}{3}$

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

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