A) \[\pi /6\]
B) \[\pi /3\]
C) \[\pi /4\]
D) \[\pi \]
Correct Answer: D
Solution :
[d] Equation \[{{z}^{6}}={{(z+1)}^{6}}\] \[\Rightarrow \,\,\,|{{z}^{6}}|\,\,=\,\,|{{(z+1)}^{6}}|\] \[\Rightarrow \,\,\,|z{{|}^{6}}\,\,=\,\,|z+1{{|}^{6}}\] \[\Rightarrow \,\,\,|z|\,\,=\,\,|z-\left( -1 \right)|\] So, z lies on the line segment joining the points 0 and \[-1\]. Hence, the roots of the equation are collinear. Given that \[{{z}_{1}},{{z}_{2}}\] and \[{{z}_{3}}\] are roots of the equation. \[\Rightarrow \,\,\,\,\arg \left( \frac{{{z}_{1}}-{{z}_{3}}}{{{z}_{2}}-{{z}_{3}}} \right)=0\] or \[\pi \]You need to login to perform this action.
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