How can I calculate something like $(i+1)^{33}$ or similar high exponent without the use of a calculator?
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Write it as an exponential. – Marra Apr 22 '13 at 18:45
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1Have you had DeMoivre's Theorem? You would re-write $i + 1 $ in "polar form" and apply that Theorem. That's pretty much what the quick way is. – colormegone Apr 22 '13 at 18:47
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HINT
Euler's formula $$e^{i \theta} = \cos(\theta) + i \sin(\theta)$$ and recall that any complex number can be written as $x+iy = r e^{i \theta}$.
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We have $1+i = \sqrt2 e^{i\pi/4}$. Hence, $$(1+i)^{33} = (\sqrt2 e^{i \pi/4})^{33} = 2^{33/2} e^{i(33 \pi/4)} = 2^{33/2} e^{i \pi/4} = 2^{16}(1+i)$$
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Not math, but about posting answers -- I'm not finding it easily on a meta search: how do you make a grey "spoiler box"? – colormegone Apr 22 '13 at 19:49
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Just the one time, or is there a terminating delimiter? And thanks! – colormegone Apr 22 '13 at 19:57
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The
Enterkey is needed to start and is also used as a delimited. I added an example here to clarify. – Apr 22 '13 at 20:02 -