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some values characterising i
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- $\displaystyle i^{\,2} \;=\; -1$
- $|i| \;=\; 1$
- $\displaystyle\arg{i} \;=\; 2n\pi\!+\!\frac{\pi}{2}$ ($n \in \mathbb{Z}$ )
- $\displaystyle\bar{i} \;=\; -i$
- $\displaystyle\frac{1}{i} \;=\; -i$
- $\displaystyle\sqrt{i} \;=\; \pm\frac{1\!+\!i}{\sqrt{2}}$
- $\displaystyle (-1)^i \;=\; e^{(2n+1)\pi}$ ($n \in \mathbb{Z}$ )
- $\displaystyle i^{\,i} \;=\; e^{2n\pi-\frac{\pi}{2}}$ ($n \in \mathbb{Z}$ )
- $\displaystyle \cos{i} \;=\; \frac{1}{2}\left(e+\frac{1}{e}\right) \;\approx\; 1.54308$
- $\displaystyle \sin{i} \;=\; \frac{i}{2}\left(e-\frac{1}{e}\right) \;\approx\; 1.17520\,i$
- $\displaystyle \cosh{i} \;=\; \cos1 \;\approx\; 0.54030$
- $\displaystyle \sinh{i} \;=\; i\,\sin1 \;\approx\; 0.84147\,i$
- $\displaystyle e^i \;=\; \cos1+i\,\sin1$
- $\displaystyle \log{i} = \left(2n\pi\!+\!\frac{\pi}{2}\right)i$ ($n \in \mathbb{Z}$ )
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"some values characterising i" is owned by pahio.
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This is version 4 of some values characterising i, born on 2008-10-30, modified 2008-11-01.
Object id is 11222, canonical name is SomeValuesCharacterisingI.
Accessed 351 times total.
Classification:
| AMS MSC: | 12D99 (Field theory and polynomials :: Real and complex fields :: Miscellaneous) |
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Pending Errata and Addenda
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