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: What is the global minimum of the function, x² 5 f(x) 3 + 2 on the interval [-2, 2] ? a) 2 b) 23 3…

A:

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…

A:

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: 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…

Q: b) Compute Re fli) when : f(2)= √Z - 1² and f(0) = -i c) Which of the following functions are…

A: Analytic function : A function f is analytic at a point complex point z=a iff the f(a) is a finite…

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

A: The solution is given below:

Q: Suppose that Q : R" → R is a quadratic form attaining the minimum value on the set ||x|| = 1. %3D…

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

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…

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

A:

Q: Prove where the following complex function is analytic

A:

Q: For each of the sets find the set of boundary points and the set of interior points. Also state if…

A: We have, (a) [0,1]U{4} (b) x,y∈ℝ2:x2+y2=1 Here we have to find the  o find: Interior Boundary…

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…

Q: write the equation for the quartic funtion ehich has zeros at -4, 1 and 3 (order 2) and passes…

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

Q: Let f(2) = |z+2|? be a complex valued function defined in a complex plane. Where is f…

A: