Solve for z- which satisfy Arg z-3-2i -6 and Arg z-3-4i -2-3

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Addition and Subtraction of Algebraic Expression

Solve for z...

Question

Solve for $z,$ which satisfy $A r g (z - 3 - 2 i) = \frac{π}{6}$ and $A r g (z - 3 - 4 i) = \frac{2 π}{3}$

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a r g (z + a) = \frac{π}{6}

a r g (z - a) = \frac{2 π}{3}, (a \in R^{+})

a r g (\frac{z - 1}{z + 1}) = \frac{π}{3}

| z | \leq 4 & A r g z = \frac{π}{3}

z

C o l u m n - I

a r g (z)

c o l u m n - I I

$C o l u m n - I$ (equation in z)	$C o l u m n - I I$ (principal value of arg(z))
$z^{2} - z + 1 = 0$	$- 2 π / 3$
$z^{2} + z + 1 = 0$	$- π / 3$
${2 z}^{2} + 1 + i \sqrt{3} = 0$	$π / 3$
${2 z}^{2} + 1 - i \sqrt{3} = 0$	$2 π / 3$

z

a r g \frac{z - 1}{z + 1} = \frac{π}{3}

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