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Old 2016-12-06, 10:26   #4
Basketry That Evening!
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"Bunslow the Bold"
Jun 2011
40<A<43 -89<O<-88

3·29·83 Posts

Originally Posted by only_human View Post
Let me take a stab at this one.

At the end of Proposition 44 is

So I can replace the radical in the denominator but I'd rather have the norm instead of the absolute value so I distribute a square from the outside exponent:
\((\frac{1}{1 + i}(1+i)^{2})^{150}\)
Then since 1 + i is not equal to zero, the expression is meaningful and I can cancel.
So I think that I get (1 + i)150

I'm not sure I am doing this right at all but I'd like to end with an apocryphal story that I like:
You are over thinking it. Re-examine proposition 47.

Because 300 % 8 == 4, the answer pretty simply follows as [spoiler]1/sqrt(2) * (-1-i)[/spoiler].

Try again you doofus known as dubslow: Because 300 % 8 == 4, the answer pretty simply follows as 4 * pi/8 = pi -> -1.

Edit: crosspost.

In the most fundamental view, exponentials are nothing more than geometry/trigonometry, and handling them as such is pretty typically the most convenient way to treat them (at least computationally in the complex plane). For more context about the fundamentality of the exponential function in the complex plane, see e.g. this wonderful little write up:

Last fiddled with by Dubslow on 2016-12-06 at 11:06
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