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A complex number z is such that \(arg(\frac{z-2}{z+2})=\frac{\pi}{3}\). The points representing this complex number lie on what?? straight line or circle or parabola or ellipse.

The centres of a set of circles, each of radius 3, lie on the circle \(x^2+y^2 = 25\). The locus of any point in the set is

Find sum of this series \(\displaystyle \sum_{r=0}^{n} (-1)^{r} \) \(^{ n }{ { { C } } }_{ r } (\frac{1}{2r}+\frac{3^r}{2^{2r}}+\frac{7^r}{2^{3r}}+\frac{15^r}{2^{4r}}.......m~terms)\)

Note by Tanishq Varshney
2 years, 5 months ago

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Should the first problem be: \(arg((z-2)/(z+2))=\pi/3\)? Then the locus is a part of a circle. Raghav Vaidyanathan · 2 years, 5 months ago

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@Raghav Vaidyanathan yes then its easy, The question was misprinted . Tanishq Varshney · 2 years, 5 months ago

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@Tanishq Varshney With z the equation is dimensionally incorrect. Rohit Shah · 2 years, 5 months ago

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