1. (a) Sketch the set S of points in the complex plane satisfying the given inequality. Determine whether the set is (1) open, (ii) closed, (iii) a domain, (iv) bounded or (v) connected. • Re(z)| > 2 I Iz - il > 1 • 2 < Re(z – 1) < 4 -1< Im(z) < 4

Q: (c) For the set A = {[0], [6]} ≤ Z12 determine the set U = h(A). Then for the set UC Z18 determine…

A: In group theory, sets like Z12​ and Z18​ are examples of cyclic groups under addition modulo 12 and…

Q: Theorem 6 If (b+ f) > (c+r) und (d+g) > (e+ s), then the necessary und sufficient condition for Eq.…

A: (P+Q)2 = P2 +Q2 + 2PQ P2 +Q2 + 2PQ = (P+Q)2 P2 +Q2  = (P+Q)2 - 2PQ

Q: 2/ If (xit) is top spaces.t x+y there are two disjoint Pen sets containing them Prove {y? y ex…

A: We use the following theorem  Arbitrary union of an Open set is open.

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Q: Show that for z, w € C: |z − w|² = |2|² + |w|² - 2 Re(wz). Sketch the set of complex numbers z EC…

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Q: positive real numbers such tha ith proof the minimum value of

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A: Since you have asked multiple questions, we will answer the first one. If you want other questions…

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Q: 6. (a) Use the Cauchy-Schwarz Inequality to prove that, for any finite sequences of complex numbers…

A: All the problems are application of Cauchy Schwarz inequality

Q: Consider the set = {x € R¹ / 93x₁ +34x2 +26x3 + 18x4 ≤ 131, X₁, X2, X Show that x₁ + x2 + x3 ≤ 2 is…

A: Here, in the question a set is given : X={x∈R4/93x1+34x2+26x3+18x4≤131, x1, x2, x3, x4 ∈ {0, 1} } We…

Q: B₁ = {(a, b): a, b are realt B₂B RIB is finite} I, is sopology generated by J₂ is Sopology generated…

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Q: 1) @ê Consider the set X = {x € R¹ / 93x₁ +34x2 +26x3 + 18x4 ≤ 131, X₁, X2, X3, X4 = {0, 1}}. Show…

A: Given: Set: X=x∈ℝ4 / 93x1+34x2+26x3+18x4≤131, x1, x2, x3, x4∈0, 1To Show: b) ConvX is a…

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Q: 5. (a) Describe and sketch the set of points in the complex plane satisfying the inequality: 1< |z…

A: The set of points shown will be bounded by two circles centered at -1,3 of radii 1 and 3.

Q: 1) (b) (c) Consider the set X = {x € R¹ / 93x1 +34x2 + 26x3 + 18x4 ≤ 131, x1, X2, X3, X4 € {0, 1}}.…

A: Given: Set, X=x∈ℝ4/93x1+34x2+26x3+18x4≤131, x1, x2, x3, x4∈0, 1We need to show that the valid…

Q: Example 9. Classify each relation as constant, linear, quadratic, or neither. a) y = x² + 5x + 6 b)…

A: The solution is given below:

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A: Given that                           Q : ℝn→ℝ is a quadratic form attaining the minimum value…

Q: EXERCISE 2: For each a/ and b/ answer these questions: (i) Sketch the set of points (directly, no…

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Q: Find all global minimum points of ƒ in R³, if ƒ (x1, x2, x3) = ex² + x½ + 2x²x3 + x² − 8x2 - 8x3

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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: 7. Which of the following equation describes the triangle inequality for complex numbers? a. b. Z₁ +…

A: (7). For complex number, the triangle inequality is |z1+z2|≤|z1|+|z2| Therefore, the answer is (a).

Q: Complex Sets 1. Sketch the following sets and determine which are domains: (a) |z2+i| ≤ 1; (b) |2z+…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

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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…

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A: According to the given data, find the equation:

Q: 1. Consider the following three domains in the space: {(x,y,z) E R³:1 ≤|x+y+z<4}, {(x,y,z) € R³ : 2…

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