URGEN taking the power of complex exponential

In summary, the rule (A^b)^c=A^(bc) does not hold for complex exponents. While it may work for positive integer powers, it can be dangerous to use with non-integer values.
  • #1
kougou
82
0

Homework Statement



e^(i*2pi*1/15) is equal to ( e^(i*2pi) )^(1/15) = (1)^(1/15)=1

Why this is false?

Homework Equations



((A)^(b))^c=A^(b*c)=A^(bc). Why this isn't the case for complex exponential?

The Attempt at a Solution

 
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  • #2
kougou said:

Homework Statement



e^(i*2pi*1/15) is equal to ( e^(i*2pi) )^(1/15) = (1)^(1/15)=1

Why this is false?

Homework Equations



((A)^(b))^c=A^(b*c)=A^(bc). Why this isn't the case for complex exponential?

The Attempt at a Solution


Because it isn't. The rule (A^b)^c=A^(bc) doesn't hold for complex exponents. As your example shows.
 
  • #3
Dick said:
Because it isn't. The rule (A^b)^c=A^(bc) doesn't hold for complex exponents. As your example shows.

But why?
When I use take the positive integer power of complex exponential, it works. What's the rule?
 
  • #4
kougou said:
But why?
When I use take the positive integer power of complex exponential, it works. What's the rule?

If b and c are integers you should be safe. If A is a positive real and one of b or c is an integer, that should also be ok. Otherwise, I think it's dangerous.
 

Related to URGEN taking the power of complex exponential

1. What is URGEN?

URGEN stands for "Universal Recursive Generator Network," and it is a computational model that uses complex exponential functions to efficiently solve problems that involve complex data.

2. How does URGEN take the power of complex exponential?

URGEN uses a combination of neural networks and mathematical algorithms to process complex exponential functions, allowing it to efficiently analyze and manipulate complex data.

3. What types of problems can URGEN solve?

URGEN is particularly effective at solving problems that involve complex data, such as pattern recognition, signal processing, and data compression. It has also been used in fields such as finance, biology, and image processing.

4. What are the benefits of using URGEN?

URGEN offers several benefits, including faster and more accurate processing of complex data, the ability to handle large amounts of data, and the potential for creating more efficient and intelligent systems.

5. How does URGEN compare to other computational models?

URGEN has been shown to outperform other computational models in certain tasks, particularly those involving complex data. Its use of complex exponential functions allows for more efficient and accurate processing, making it a valuable tool in scientific research and problem-solving.

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