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What was the difference between the formula that Roger cotes derived and that euler got? I mean to say that Euler got the following formula : $$e^{ix} = \cos x+i \sin x$$

And Cotes got the following : $$ix = \ln(\cos x + i\sin x)$$

We can directly see that it is same as euler's

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    $\begingroup$ Well, to be precise, the first form holds for all $x\in\mathbb{R}$, while the second cannot hold for all $x\in\mathbb{R}$ $\endgroup$
    – user228113
    Jun 7, 2015 at 14:15

1 Answer 1

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The problem is that the complex logarithm is multivalued under the current definition. Therefore Cotes' formula is not really true anymore, but it was when he got it.

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