O Plot the followring sets on the complex plane:

Q: Sketch the curve in the complex plane given by | Z-3| = | 7 + 3i } %3D i, z'+ 2?= 2. %3D

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Q: Ihe complex number z is defined by z = a + ib, where a and b are real. The complex is denoted by z*.…

A: Given: z=a+ib, z*=a-ib

Q: Find the set of points z in the complex plane that satisfies each of the following (i) |z| = Rez+2…

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Q: Verify that U(x,y) = x3y - xy3 is harmonic on the complex plane.

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Q: Find and sketch the sets in the complex plane given by (1) z – 3 +|z+3=10 (2) |Arg(z)|< r/ 2

A: It is required to find and sketch the sets in the complex plane (1) z-3+z+3=10 Take z=x+iy Then…

Q: 2. Shade and describe in words the set in the complex plane: Determine whether the set is a domain.…

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Q: If Zo is any complex number interior to any simple closed contour prove that dz 2πί, η- 1 Jc (z-…

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Q: Apply Cauchy's conditions, Check if the complex function is analytic or not f(z)=sin(z)

A: use cauchy - riemann equation to show sinz is analytic...

Q: | Re(z) |> 1 | 2 – i< 3 1</ z + i+1|< 2

A: As per our guideline we are allowed to do 1 question or maximum 3 subparts at a time. Please post…

Q: Describe the set of points z in the complex plane that satisfies | z + 1 - i | = 1. please show…

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Q: (b) If z = x + iy is a complex number. Sketch the curves in the complex plane given by i. Im(2) = –1…

A: i. Given that Imz=-1. This implies that, Imz=-1Imx+iy=-1y=-1 Sketch the curve Imz=-1 as shown below.

Q: 26 Jlguill The conjugate of complex number z satisfy: Z-z=2ilmz O z +z=2Rez O

A: the conjugate of complex number z satisfies

Q: 29. When z = z If z and z are equal, what can you say about the location of the point z in the…

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Q: Show that x+iy | g+ix / = 1₁ =1, where X +iy and y+ix are complex numbers.

A: Here, let evaluate x+iyy+ix Using the absolute rule ab=|a||b|: =|x+iy||y+ix|

Q: z = e2x+3iy

A: The given complex number is  z = e2x + 3iy

Q: Find the set of points satisfying the equation in the complex variable z: |z* + 2i| = I(z − 3i)|…

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Q: Sicetch the complex plane given by 2.

A: (1) z-3=z+3i Put z=x+iy, we get…

Q: i) ii) (AB) = B*A', ii)AA)* = TA', (A+B)* = A* + B', %3D %3D %3D where A is a complex number and At…

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Q: then find (An B C). Z, +Z3 1-i3 Z2 - Z3 (B) right angled isosceles (D) obtuse angled 7. The complex…

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Q: H.W-1:Find and sketch the sets in the complex plane given by (2) |Arg(z)< t/ 2

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Q: z is a complex variable z=x+iy pic attached with question  Evaluate using L’Hospital’s rule

A: To calculate the limit of the given indeterminate form using L'Hosptial rule

Q: Discuss the analyticity of the function S(2) = z + z² in complex plane, where i is the complex…

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Q: H.W-1:Find and sketch the sets in the complex plane given by (1) z – 3 +|2+ 3=10 (2) |Arg(z)< t/ 2 1…

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Q: H.W-1:Find and sketch the sets in the complex plane given by (1) z – 3|+|z+3=10

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Q: Argand plane. Label properly. 2. Represent the following complex numbers on one A = 1+1 B = 1- C =…

A: Given that: A=1+iB=1-iC=-3+4iD=-3-4i

Q: ii. ?² + ?̅²= 2

A: I am providing the solution of (ii) only.

Q: 6:29 A docs.google.com Let z be a complex number and f(z) be any function. If C is a closed contour…

A: ∮ Im (f(z)) dz (equal to the above)

Q: Exercise 3. Let z be a complex number. Then i(cosh(3z) + sinh(3z)) a. ie3z b. ie- -3z с. е 32 d.…

A: we define the hyperbolic sine function by sinh(z) = ez−e-z 2 and the hyperbolic cosine function by…

Q: Draw the set of points z on the complex plane such that V 2i · z is real. Explain your answer.

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Q: Find the set of points z in the complex plane that satisfies each of the following (i) z = Rez+2…

A: The complex number is expressed in the form of  Then the absolute value of the complex number is…

Q: Find the distance between the points 2+3i and 5 -2i in the complex plane. (Round your answer two…

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Q: (b) Shade the region in the complex plane defined by z+1+i 2-1-5i

A: Solution:-

Q: Plot the points z = 3+9i and w = 7+5i on a complex plane ană find distance between

A: Plot the points z = 3+9i and w = 7+5i

Q: Sket ch the curve in the complex plane given by 1z-3| = | 2+ 3il %3D

A: Just solve by using defination of mudulus of z.

Q: Ecample 12: Show that the equation of a straight line in the Argand plane can be put in e form zb +…

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Q: Find the set of points satisfying the equation in the complex variable z: |z* + 2i| = |F(z – 3i)|…

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Q: Let z be a complex variable, z=x+iy Deacribe graphically the region represented be the following:…

A: In terms of simplifying everything, let z=x+iy∈Sz=x+iy∈S, for some x,y∈Rx,y∈R. First we plug…

Q: Draw/Describe the set of points in the complex plane that satisfies |2z – i| = 4.

A: Let the complex number,  z=x+iy . The expression, |z| is calculated using the formula, |z|=x2+y2 .

Q: a) Describe the set of points z in the complex plane that satisfy the given equation Iz + (P + 1)i|…

A: a) Describe the set of point z in the complex plane that satisfy the given equation  z+(P+1)i =…

Q: find the ser of Points Zinthe complex Plane that Satisfy the given equation. 12-31 = Rele) %3D

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Q: Answer the Following: 1. describe the set of points z in the complex plane that satisfy (a) =:-1 (b)…

A: Complex representation in argand plane

Q: Let z be a complex number such that Iz| = 4 and arg(z) = 5T/6, then z = (a) -2v3 + 2i (b) 2v3 + 2i…

A: Recall:    Let z=x+iy be an complex number then             z=r(cosθ +i sinθ)…

Q: b) Integrate the above via partial frachion decomposition 6ver the complex numbers" X= - b b2-4ac X…

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Q: Apply Cauchy's conditions, check if the complex function is analytic or not. f(z) = ze-z

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Q: Write out the conjugate for the complex mumbers i. 25+15i ii. -14 iii. -4-5

A: According to the given information, it is required to write the conjugate of the complex number.

Q: Scetch the following sets in the complex plane: a) {2 € C; z = i2}; b) {2 € C; log(2) € (0, 1]}.

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Q: Plhet Ziand Zz aretwo complex numbers Such that Z1 = -2+2i, Zz Find arg 3 -2-27

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Q: 10 Consider the set of points described by =+2=1 on the complex plane. What is the maximum value of…

A: Given- z+2=1 To find- The maximum value of arg z.