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Rectangle

Z 1 and z 2 a...

Question

$z_{1}$ and $z_{2}$ are two adjacent vertices of a regular polygon with centre z. Find the angle made by one side at the centre.

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Solution

The correct option is C

The angle made by one side looks like in the above figure. From the figure its clear that we get $z_{2}$ by

rotating $z_{1}$ by an angle of θ anticlockwise about z. So we have

$\frac{z_{2} - z}{z_{1} - z}$ = $e^{i θ}$

$θ$ = arg $(\frac{z_{2} - z}{z_{1} - z})$

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Similar questions

| z - z_{1} | = a

| z - z_{2} | = b

z, z_{1}, z_{2}

| z - z_{1} | - | z - z_{2} | < | z_{2} - z_{1} |

\Rightarrow z

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Z = 0

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Z_{2} =

z_{2} = {\bar{z}}_{1}

z_{2} = \frac{1}{z_{1}}

| z - z_{1} | + | z - z_{2} | = k (> | z_{1} - z_{2} |)

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| z - z_{1} | = | z - z_{2} |

| z - (z_{1} + z_{2}) / 2 | \leq r

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