Define harmonic function. Prove that the function u = 3x²y+ 2x² – y³ – 2y² is harmonic. Find its harmonic conjugate v and express u+iv as an analytic function of z.

Q: 4. Find two possible non-linear functions & and such that goh= √sinx-x²

A: To find the non linear function by the given composition.

Q: f(x, y, z) = x-y y²+2y+z²-4

A: We have shown that the domain is all of R3 except the points on the surface of infinite length…

Q: tate and Prove Euler's Theorem on homogeneous functions.

A: Statement :                       Euler's theorem states that if f is a homogeneous function of…

Q: Determine whether the pair of functions is linearly independent or linearly dependent on the real…

A:

Q: The following function is injective or not?  s : C → C, s(z) = z^2 (Note: C means the complex…

A: Given the function S:ℂ→ℂ by S(z)=z2. Determine whether the function S is injective.

Q: Suppose that Nolan throws a baseball to Ryan and that the baseball leaves Nolan's hand at the same…

A:

Q: Write the function f(x) = √1 + x² as a polar function.

A: Let

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A: ddxxn=n xn-1

Q: Find the standard factorization of the entire function f(z) = cosyz

A: Using the Euler's formula as, cosθ+isinθ=eiθcosθ-isinθ=e-iθ Now adding both the equations,…

Q: f(x, y) = x² + y² + 64xy

A: