DERIVATIVE OF A FUNCTION OF COMPLEX 1. Express the complex number (-1 + 1)' in the form x + iy. 2. Test the function f(2) = Iz}² for differentiability. 3. Apply the Cauchy-Riemann conditions to determine if f(2) = z* is differentiable.

Q: If Z1 =1- j3, Z2=-2+ j5 andZ3 =-3- j4, determine in a + jb form: Z1Z2Z3 О а. -5- ј85 О Б. 5+]85 О…

A: We have to multiply the given three complex numbers.

Q: Question For j(x) = f(x) · g(x), use the product rule to find j'(-8) if f(-8) = 2,f'(-8) = -2, g(-8)…

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Q: (8) Given x²/3-y²/3 - y = 3, find ae equation of the tangent line at the point (1,-1).

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Q: Find the 3rd derivative of the function y (2z-8z2 +3) (z+3) O y"=120z2 192z + 42 120, 198z + 72 =…

A: We need to find the 3rd derivative of y=2x3-8x2+3x2+3 . So,      y'=2x3-8x2+3x2+3'…

Q: B) Find all of the second derivatives for f(x, y) = (3xy2 + 2xy + x²) In; x²+y² itable graph and…

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Q: An analytic function of a complex variable z = x + iy is expressed as f(z) = u(x, y) + iv(x, y).…

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Q: 1. (x*+2x)°(6x²+4)dx 2. [3x²+2x+1 dx 3. (x?)/(x³-4) dx 4. (x+1)/(\x²+2x+1) dx

A: As per the guidelines we can solve 3 problems only.

Q: 6. Express the following functions in the form u(r, y) + iv(r,y). (a) f(z) = +(1– 2i)z. %3D (b) f(2)…

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Q: The graph of the function f(x) = sin(x + 4) is shown along with the points ( − 4, ƒ( − 4)) and ( −…

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Q: Let f(2)= iz³ + cos(z²) z² +1 i. Find f'(z). ii. Evaluate ƒ'(–2i) and simplify. iii. State the…

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Q: B3. (a) Let y be a function of x, defined implicitly by the equation x?y + y3 + x = 0. Find the…

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Q: y = CLe? + C2 ze? (3) Differentiate with sespect to 'x' get we dy Again differentiate with sespect…

A: Some results are required to understand the differentiation in the given problem.

Q: Q. No.1 a) Use logarithmic differentiation to find dy/dx of the expression: 3 2(2x+1)(x-3)…

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

Q: 47. Show that y = x³ + 3x + 1 satisfies y"" + xy" - 2y = 0.

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Q: - 4( Let u(t) = 8t i+ (-9)j-8k and v(t)= e'i+9 ej- e "k. Compute the derivative of the following…

A: topic - dot product and derivative of a function

Q: For which z values of the complex functions given below have the derivative (f'(z)), obtain a) f(z)…

A: The derivative of A function f at z=z0 is defined as  If f is polynomial in z , then f is…

Q: Find the directions in which the function increases and decreases most rapidly at Po. Then find the…

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Q: The directional derivative of the function function = x - xyz + y? at the point (1, 2, -1) in the…

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Q: Q2) Determine using Cauchy Riemann equations the function below is analytic or not? 2z4-8z5+4z6…

A: If f(z)=u(x,y)+iv(x,y) then Cauchy-Riemann Equations is ∂u/∂x=∂v/∂y and ∂u/∂y=−∂v/∂x

Q: In(x+xy+y) 1

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Q: Find f'(z) when f(z) = J, 0, if z = 0 if z = 0

A: fz=z¯ 2zif z≠00if z=0 To Find: f'z