Find the complex number z if arg(z+1)=(π/3) arg(z−1)=((4π)/3)


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Question Number 39708 by NECx last updated on 10/Jul/18

$F i n d t h e c o m p l e x n u m b e r z i f$ $a r g (z + 1) = \frac{π}{3}$ $a r g (z - 1) = \frac{4 π}{3}$
	Answered by MrW3 last updated on 10/Jul/18

	$l e t z = a + b i$ $(1)$ $\frac{b}{a + 1} = \tan \frac{π}{3} = \sqrt{3}$ $\Rightarrow b = \sqrt{3} (a + 1)$ $\Rightarrow z = a + (a + 1) \sqrt{3} i, a ⩾ - 1$ $(2)$ $\frac{b}{a - 1} = \tan \frac{π}{3} = \sqrt{3}$ $\Rightarrow b = (a - 1) \sqrt{3}$ $\Rightarrow z = a + (a - 1) \sqrt{3} i, a ⩽ 1$
	Commented by MrW3 last updated on 10/Jul/18

	Commented by NECx last updated on 10/Jul/18

	$T h a n k y o u s o m u c h s i r$
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