Is (-i)^(-m) Equal to cos((m*pi)/2)+i*sin((m*pi)/2) in Complex Analysis?

In summary, a relation in complex analysis is a set of ordered pairs that describes the connections between complex numbers. It is a generalization of a function, where an input can have multiple corresponding outputs. Relations are important in studying complex functions and understanding the connections between points on the complex plane. A relation is considered symmetric if the order of the input and output pairs can be reversed and the relation still holds. It is not possible for a relation to be both reflexive and anti-symmetric at the same time.
  • #1
dado033
5
0
is this relashion true? or false?
if it is true how can I proof it?
(-i)^(-m) = cos((m*pi)/2)+i*sin((m*pi)/2)
 
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  • #2
Perhaps try showing the left hand side is periodic. Then I think this would mean that you would only have to work out a finite number of cases.
 
  • #3
dado033 said:
is this relashion true? or false?
if it is true how can I proof it?
(-i)^(-m) = cos((m*pi)/2)+i*sin((m*pi)/2)


-i=exp(-i(pi/2))
Therefore (-i)^(-m)=exp(i(m*pi/2))
Now apply Euler's identity.
 
  • #4
thank u very much
 

Related to Is (-i)^(-m) Equal to cos((m*pi)/2)+i*sin((m*pi)/2) in Complex Analysis?

1. What is a relation in complex analysis?

A relation in complex analysis is a set of ordered pairs that represents the correspondence between two sets of complex numbers. It is used to describe the connections between different elements in a complex function or equation.

2. How is a relation different from a function in complex analysis?

A relation can be seen as a generalization of a function, where a function is a specific type of relation that assigns exactly one output for each input. In a relation, an input can have multiple corresponding outputs, whereas in a function, each input has only one output.

3. What is the importance of relations in complex analysis?

Relations are important in complex analysis because they allow us to study the behavior and properties of complex functions. They also help us to understand the connections between different points on the complex plane and how they relate to each other.

4. How do you determine if a relation is symmetric?

A relation in complex analysis is considered symmetric if for every input-output pair (a, b) in the relation, there exists an input-output pair (b, a) in the relation as well. In other words, if the order of the input and output can be reversed and the relation still holds, then it is symmetric.

5. Can a relation be both reflexive and anti-symmetric?

No, a relation cannot be both reflexive and anti-symmetric at the same time. A relation is reflexive if every element is related to itself, and anti-symmetric if no distinct elements are related to each other. These two properties are contradictory, so a relation cannot have both at the same time.

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