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Sinh / sin

  • Thread starter struggles
  • Start date
  • #1
50
0

Homework Statement


So this is a really simple problem and i know I'm missing something really obvious but i just can't spot it.

Screen Shot 2016-05-16 at 15.48.10.png


Homework Equations




The Attempt at a Solution


so in the second part above I get :
e-x - ex/2i. However I don't get the next bit as the 2i on the denominator is now factored into the top equation to give -ie-x + iex/2. I don't get how the 2 equations are equivalent and what they've done to get the i from the denominator to the numerator. If anyone could explain how this happened that'd be great!
 

Answers and Replies

  • #2
12,654
9,181
What is i?
 
  • #3
941
394
Do you know what ##1/i## is?
 
  • #4
50
0
  • #5
12,654
9,181
i-1?
First answer my question and then use it to answer struggles'. ##i^{-1}## is simply another form of ##\frac{1}{i}## which doesn't really help.
 
  • #6
robphy
Science Advisor
Homework Helper
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Suppose you didn't know what ##i## is
but it seems that (from your second equals sign) ##\frac {1}{i}= -i##... what must ##i## satisfy?
 
  • #7
12,654
9,181
Suppose you didn't know what ##i## is
but it seems that (from your second equals sign) ##\frac {1}{i}= -i##... what must ##i## satisfy?
How is it defined? What stands ##i## for? There must have been some explanation for it.
Remark: Sorry, for confusing your names, struggles and axmls!
 
  • #8
941
394
Though it isn't obvious that this is the way to find this, here's a hint:
$$\frac{1}{i} = \frac{1}{i} \frac{i}{i}$$
 
  • #9
50
0
so i = √-1 so i2 = -1. so 1/i must equal 1/(-1)1/2 = (-1)-1/2? is that what you were getting at fresh-_42?
So axmls 1/i = i/i^2 = -i! Thanks both of you!
 

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