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

#Algebra

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

@Brian Charlesworth @Caleb Townsend

Tanishq Varshney - 6 years, 2 months ago

@Ronak Agarwal @Mvs Saketh @Raghav Vaidyanathan @Krishna Sharma @Karan Shekhawat

Tanishq Varshney - 6 years, 2 months ago

Should the first problem be: $arg((z-2)/(z+2))=\pi/3$ ? Then the locus is a part of a circle.

Raghav Vaidyanathan - 6 years, 2 months ago

yes then its easy, The question was misprinted .

Tanishq Varshney - 6 years, 2 months ago

With z the equation is dimensionally incorrect.

Rohit Shah - 6 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$