# 1700 Followers problem!

Algebra Level 5

Consider two complex numbers: $$z_1$$ : $$692+3745\sqrt{3}i$$ and $$z_2$$ : $$692+1729\sqrt{3}i$$.

There exists another complex number $$z$$ such that $$\text{arg}\left(\dfrac{z-z_1}{z-z_2}\right)=\dfrac{\pi}{3}$$.

Then , Find the value of $$|z+316-2737\sqrt{3}i|$$

Details And Assumptions:

• $$\text{arg}(z)$$ is the argument which means the angle made by the complex number $$z$$ with the positive X axis.
• $$|z|$$ represents the modulus of complex number $$z$$.
• $$i=\sqrt{-1}$$
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