Complex Analysis (MP23CC1) - Quiz II

• None of these

• 0

• The residue of f(z) at z=a is given by f(a).
• The residue of f(z) at z=a is always zero.
• The residue of f(z) at z=a is calculated using the integral of f(z) around a.
• The residue of f(z) at z=a is given by Res(f, a) = lim (z -> a) (z - a) f(z).

what does the argument principle shows that

• The argument principle shows the relationship between the number of zeros and poles of a function within a contour.
• It provides a method for calculating integrals along a contour.
• It shows the continuity of a function over a contour.
• It demonstrates the symmetry of poles and zeros in complex functions.

what is the meaning behind the statement of Rouche's Theorem

• Rouche's Theorem states that all complex functions have at least one zero.
• Rouche's Theorem is used to find the maximum value of a function on a contour.
• Rouche's Theorem applies only to real-valued functions and their derivatives.
• Rouche's Theorem provides a method to count the zeros of complex functions within a contour by comparing them to another function.

Among the following, which one is the simplest harmonic function?

• Constant function
• Linear function
• Exponential function
• Sine function