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The center of a regular polygon of n sid...

The center of a regular polygon of n sides is located at the point z=0, and one of its vertex `z_(1)` is known. If `z_(2)` be the vertex adjacent to `z_(1)`, then `z_(2)` is equal to

Text Solution

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Let A be the vertex with affix `z_(1)`.

`z_(2)` can be obtained by rotating `z_(1)` through `2pi//n` either in clockwise or in anticlokwise direction. Therefore,
`(z_(2))/(z_(1))|(z_(2))/(z_(1))|e^(pm(2pi)/(n))`
or `z_(2) = z_(1) e^(pm(2pi)/(3))" "[because |z_(2)|=|z_(1)|]`
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