| Re(z) |> 1 | 2 – i< 3 1

Q: This is question of Complex Analysis.

A: I am providing the solution of (ii) only as follows below :

Q: The complex numbers 0, z+ 1 and z2 are distinct and collinear on the complex plane. Draw the locus…

A: As per our guideline we are supposed to answer only first question of a multiple type questions.…

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

A: here we can use directly definition or properties of curve to find that which curve is represented…

Q: a) Use DeMoivre's theorem to find all roots of: w3 = Z = -27 in the complex plane.

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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: 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: a) it is entire in C (complex plane) and has at least two zeros, which are az and a2. b) Evaluate fe…

A: a) We put a1=1 and a2=-1. Consider f(z)=(z-1)(z+1). Two zeros of this function are 1 and -1.

Q: Find all solutions of z E C of the equation i(z + 2i)4 = -81 and hence show via the sketch all these…

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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: Which of the following represents the region of the complex plane defined by |z−2i-3| ≤2? (A)…

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Q: Find the complex conjugate z of z1 = -2+ 8i. %3D %3D

A: We have to find the complex conjugate {\displaystyle {\overline {z}}}1 of  z1 = -2 + 8i

Q: 1. Graph the following numbers on the complex plane: - i) 2+3i 2-3i iii) -2-31 iv) -2+3i 3 4 v) -6…

A: Complex plane: The collection of a complex number represented on a plane. it is also known as an arg…

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: 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: Describe the following points on the complex plane: (f) i3z = 2-',

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Q: Sketch the in the complex curve plane given by.- i) |2 -31 12+3i/ %3D

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Q: 2. Show that z^2 is one-to-one in a domain D if and only if D is contained in a half-plane whose…

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Q: 1- The distance between two complex numbers z1 Z2 is denoted by: a) Iz – z2| b) /x + y c) Vz, + z2…

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Q: Sketch the set S of points in the complex plane satisfying the given inequality. Determine whether…

A: To find- Sketch the set S of points in the complex plane satisfying the given inequality. Determine…

Q: 7. Let z = -3 + 5i. Plot the points z,-z,7,-ž and - in the complex plane.

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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: The set of all complex numbers is denoted by C={x+iy:x,y€R}

A: A complex number is the combination of real and imaginary number in the form of x+iy , x, y are real…

Q: Find all non - zero complex numbers z satisfying z =i z.

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Q: Let z be a complex number. Then sinh(2z)-i is bounded in C.* False True

A: Given a statement

Q: 1. Describe and sketch the curve in the complex plane given by 2|z| = |z-2| Also write your final…

A: We have to Describe and sketch the curve in the complex plane given by2|z| = |z-2|Also write your…

Q: Describe graphically the regions of the complex plane represented by each of the following…

A: Formula: a+ib=a2+b2 (a) 1&lt;z+i≤2 Let z=x+iy be a complex number in the region. Hence,…

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: Find the centre and radius of the circle formed by all the points represented by z = x+ iy…

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Q: Which of the following represents the region of the complex plane defined by |z+1-2i| > 3? (A) (C)…

A: A detailed solution is given below.

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

A: Solution:-

Q: describe the set of points z in the complex plane that satisfy (a) E= 2-1 (b) z- i = 2 |2 - 1|

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

Q: Find the centre and radius of the circle formed by all the points represented by z = x+ iy…

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Q: Let z be a complex number such that z, z3 and z5 form an equilateral triangle on the complex plane.…

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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: a) Find the equation of the plane th

A: The question is taken from the plane in which we have to find the equation of the plane and integral…

Q: Find the cube root of Z^3=8i lying in the first quadrant of the complex plane. " i-V3 O 2i+v3 i+2/3…

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Q: 10. Let z₁ and z₂ denote complex numbers. Show that (Z₁, Z₂) = Z₁ Z₂ defines an inner product, which…

A: Z1 and Z2 are orthogonal iff &lt;Z1, Z2&gt; = 0

Q: Find the complex conjugate z of z1 = -1+5i. %3D

A: Given that z1=-1+5i find the complex conjugate

Q: 33. , Given that the complex numbers z - 3 + i and z2 = -3 - i are such that Iz - z,|-|z – z2 l. The…

A: Here we find locus of z

Q: 1. Graph the following numbers on the complex plane: - i) iii) -2-3i i) 2+3i 2-31 iv) -2+ 3i v) -6…

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Q: Consider the region defined by z 0 (i.e. the entire complex plane except for the origin, which is…

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Q: 2. Describe and plot the points z in a complex plane defined by the following region: A = {z in C :…

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Q: 15. On the Argand plane, carefully sketch the set of complex numbers, z, that satisfy the condi-…

A: Consider the given condition, z=argz Let's consider that the argument is principal argument and…

Q: Let z be a complex number such that Iz| = 4 and arg(z) = 5Tt/6, %3D * = then z

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Q: Let z be a complex number. Then sinh(2z)-i is bounded in C. * False True

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