(a) Evaluate the integral: O f(2) dz , where f(z) = z and C is the closed path defined as the square with vertices (corners) at 1 – i, 1+ i, –1 +i and -1 – i. (b) Evaluate the integral of f(z) = z (also denoted as z* in class) along the same closed path.
Quadratic Equation
When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations and their types.
Demand and Supply Function
The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to understand the consumer behavior. The evaluation of supply side factors is important for the consumers in order to understand that what kind of combination of goods or what kind of goods and services he or she should consume in order to maximize his utility and minimize the cost. Therefore, in microeconomics both of these concepts are extremely important in order to have an idea that what exactly is going on in the economy.
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![### Complex Analysis Exercise
#### Problem Statement
**(a)** Evaluate the integral:
\[
\oint_C f(z) \, dz,
\]
where \( f(z) = z \) and \( C \) is the closed path defined as the square with vertices (corners) at \( 1 - i \), \( 1 + i \), \( -1 + i \), and \( -1 - i \).
**(b)** Evaluate the integral of \( f(z) = \overline{z} \) (also denoted as \( z^* \) in class) along the same closed path.
#### Explanation of Diagrams
There are no specific diagrams or graphs included in the given text. The text defines a closed path \( C \) in the complex plane that forms a square. The vertices of this square are given by the complex numbers \( 1 - i \), \( 1 + i \), \( -1 + i \), and \( -1 - i \).
This setup implies a square centered at the origin with sides parallel to the real and imaginary axes, having a side length of 2 units.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1fcc62d3-a3e3-4e53-b591-f5755305bd07%2Fa48ff795-9730-4c3e-a94c-5a436a30ac6a%2Fzhp8qy7_processed.jpeg&w=3840&q=75)
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