(1+i)^100

[rickere]

I need help with this problem, it's a bonus take home quiz from my calculus teacher, and he has given the class the answer, but we need to show work to get the points, so here it is.
(1+i)^100 = -2^50

 

[pka]

This all you need to know to work this problem:
\(\displaystyle \L \begin{array}{l}
a + bi = rcis(\beta )\quad \Rightarrow \quad \left( {a + bi} \right)^n = r^n cis\left( {n\beta } \right) \\
1 + i = \sqrt 2 cis\left( {\frac{\pi }{4}} \right) \\
\end{array}\).

Now if you want to see a completely worked out solution that you can just hand in for full credit, just wait.

 

[rickere]

I'm still not understanding it

 

[morson]

(1 + i)^100 =

(sqrt2 * cis[pi/4])^100 = (2^1/2)^100 * cis(100*pi/4), by de Moivre's theorem

= 2^50 * cis(25pi) = 2^50 * cis(pi) = 2^50 * (cos(pi) + isin(pi))

= 2^50 * (-1 + 0) = -2^50

 

[pka]

I need help with this problem, it's a bonus take home quiz from my calculus teacher

morson, who should get the extra credit for your work?

 

[morson]

He or she wrote that they didn't really understand it, so I gave a worked solution. :?

 

[stapel]

He or she wrote that they didn't really understand it, so I gave a worked solution.

But I would think that the point of the take-home quiz was probably that the student figure it out himself. The instructor was likely giving the student the opportunity to do some self-study in order to earn some extra credit, not to find some place where he could copy down the answer without thinking or learning.

Just my opinion, of course; I could be wrong....

Eliz.

 

[tkhunny]

While I'm here, I may as well weigh in on the "related example" and "leading question" doctrine.

Old Addage: Give a fish or Teach to fish?

 

[rickere]

Thought the point of this site was to help people with their math problems... I did work on this problem for quite some time.. used the formula pka gave, didn't know what it all meant.. so i asked for more help... didn't mean to get everyone fired up

 

[tkhunny]

No one is fired up. "Help" is a hard thing to define.

The most unlcear methodology used in attempting to help, where one gains the very least information about the student or about any benefit to the student, is simply to work the problem and show a complete solution.

The more you communicate, the more we understand each other.