Problem 3: Consider the following Complex Numbers, and calculate the following: Z=8-25i 22=-2+41 a. Z1 Z2...

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Problem 3: Consider the following Complex Numbers, and calculate the following: Z=8-25i 22=-2+41 a. Z1 Z2 b. z c. Express both complex numbers in Polar Form. Show all your work MECE 3449-02: Mechanical Engineering Analysis I The University of Texas Rio Grande Valley-Spring 2022 Problem 4: Consider the following general Complex Function. f(z) = u(x, y) + iv(x, y) a) If u(x,y) = x- y and v(x, y) = 2xy, are the Cauchy-Riemann equations satisfied? Show all your work b) If the function is analytic, prove that u(x, y) and v(x, y) are harmonic functions using Laplace equations. Show all your work. Problem 5: Consider the following complex numbers in Polar Form: 21 = 20'(-) 22 = 80') a) Express z and z in Rectangular Form Problem 3: Consider the following Complex Numbers, and calculate the following: Z=8-25i 22=-2+41 a. Z1 Z2 b. z c. Express both complex numbers in Polar Form. Show all your work MECE 3449-02: Mechanical Engineering Analysis I The University of Texas Rio Grande Valley-Spring 2022 Problem 4: Consider the following general Complex Function. f(z) = u(x, y) + iv(x, y) a) If u(x,y) = x- y and v(x, y) = 2xy, are the Cauchy-Riemann equations satisfied? Show all your work b) If the function is analytic, prove that u(x, y) and v(x, y) are harmonic functions using Laplace equations. Show all your work. Problem 5: Consider the following complex numbers in Polar Form: 21 = 20'(-) 22 = 80') a) Express z and z in Rectangular Form