Number of complex numbers z such that left| z right| + z - 3bar z = 0 is equal to

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4-1.Complex numbers

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Number of complex numbers $z$ such that $\left| z \right| + z - 3\bar z = 0$ is equal to

A

$0$

B

$1$

C

$2$

D

$3$

Solution

Let $z=x+i y$

$\sqrt{x^{2}+y^{2}}+x+i y-3 x+3 i y=0$

$y=0$ and $\sqrt{x^{2}+y^{2}}=2 x$

$x=0$

$(0,0)$ is only possiblity

Standard 11

Mathematics

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