1. Describe geometrically the sets of points z in the complex plane defined by the following relations: (d) Re(z) > c, (resp., 2 c) where e ER. (e) Re(az + b) >0 where a, b E C. (f) | Re(z) + 1. (g) Im(z)e with CER. =

Q: mplex function f(z) = z(z-21) have a removable

A:

Q: Use Stoke's Theorem to evaluate Į F· dr where F (x, y, =) = , and C is the triangle with C vertices…

A: given Fx,y,z=z2,y2,xy ⇒Fx,y,z=z2i^+y2j^+xyk^ and a traingle C with vertices 1,0,0 ,0,1,0 ,0,0,2 to…

Q: Let f(2) = Re(z) be a complex valued function defined on a complex plane С. Where is f…

A:

Q: Explain why the fundamental theorem of algebra does not apply to f(x) = Vx + 3. That is, no complex…

A:

Q: Let z be a complex number and f(z) be any function. If C is a contour and Sc F(2)dz = 0 then None of…

A: We have to use Morera's Theorem to choose correct option.

Q: Let z be a complex number, f(z) be any function, and C be any contour. Then Sc F(z)dz+ S_cf(z)dz is…

A:

Q: 1 -2 4 17. Let a 4 a2 -3 and b : For what 7 value(s) of h is b in the plane spanned by aj and a2?

A:

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

A:

Q: Find the locus of the points z that satisfies 3(22 + z?) + (8 – 16i)z + (8+ 16i)z – 10|z|? = 16.

A:

Q: Discuss the analyticity of the function f(=)= zī + Z in complex plane, where z is the complex…

A:

Q: Let (x, y) eRx R. Consider the following functions from R? to R? r((x, y)) = (-y, x) and s(x, y)) =…

A: This is a problem of multivariable Calculus.

Q: The function f(z) is complex valued in the complex plane. f(z) is bounded and entire. Prove that…

A: As per the Louisville's theorem, every entire function which is bounded must be constant. Use the…

Q: f(-2)=3 f'(-2) = 4 g (4) = 5 g (4) = 2 The point (-2,4) lies on the curve in the xy-plane given by…

A: f(-2)=3f'(-2)=4g(4)=5g'(4)=2

Q: ii. z2 +2 = 2.

A: I am providing the solution of (ii) only. The detailed solution is as follows:

Q: Let f(2) = Ln(2² + 1). Find a possible arrangement of the branch cut of f(2) on the complex plane.

A: Given: f(z)=Ln (z2+1)

Q: Fill in the blanks: 1) In general if f(z) and its conjugate are both analytic in a given domain D…

A: 1)  In general if f(z) and its conjugate are both analytic in a given domain D then f(z) must be…

Q: sketch the set S of points in the complex plane satisfying Im(z) < Re(z)

A:

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

A:

Q: (1) z – 3 +|z + 3} =10 (2) |Arg(z)< t/ 2 Arg(z) s (3) Re <1

A:

Q: Let C2 be the boundary of the triangle whose vertices are (1, 2), (-3, 1), and (-2, 2). Suppose C2…

A:

Q: Find a plane containing the lines x = 3+ 21 x =1- 21 y = 4– 31 and y = 7+41 where -o <t<00, z =1-31.…

A:

Q: Let f(x,y)=√√9-x²-3y² State the domain off and sketch it in the x-y plane. The domain must be…

A:

Q: 6. Consider F (w), a complex function of a real variable w: F (w) = (2+jw)/(3+j4w) a. Express F (w)…

A: Given: The complex function of a real variable .a) To express  in cartesian form and find it's real…

Q: b) A function f is analytic on the domain {|z| > 2}. It also satisfies |f(z)\ < 1/\z|. Let C be the…

A: We are given the following. A function f is analytic on the domain |z|&gt;2. It also satisfies…

Q: Let ƒ(z) = |z|², z € C. Show that f is complex-differentiable at z = 0, but nowhere else.

A:

Q: Let f(z)=y-2xy +i(-x+x² - y²)+z² where, z=x+iy is a complex variable defined in the whole complex…

A:

Q: Use the Cauchy-Riemann PDES to determine all points z =z+ iy € C in which the following functions…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 12. (a) Describe the set of points in the complex plane that satisfies |z + il + |z – i| – 1= 0. (b)…

A:

Q: 14) Find and graph of the roots in the complex plane for Vi 15) Let u = x³y - y³x a. Verify that the…

A:

Q: Let z be a complex number and f(z) be any function. If C is a contour and Sc f(z)dz = 0 then

A: By cauchy theorem in complex integration:-

Q: Consider the set C of complex numbers. Let (c², d) be a function where c² represents an element from…

A:

Q: Sketch the set of points in the plane which satisfy the equation y + 2 = 3(x − 4)

A: We have to draw the graph for y+2=3(x-4)

Q: Let z be a complex number and f(z) be any function. If C is a closed contour then Im. f(z)dz is $.…

A:

Q: 7. Which of the following equation describes the triangle inequality for complex numbers? a. b. c.…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…