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Complex Analysis

Multiplication of Complex Numbers

Find the product. Write the product in rectangular form, using exact values. [8 cis 210°] [6 cis 330°1] Which is the correct answer? a) 24i b) -12 + 12 x square root of 3i c) -48 d) 12 x square root of (3 + 12i)

Write the complex number in rectangular form.

Write the complex number in rectangular form. cis 210° Which is the correct answer? a) -square root of 3/2 + i1/2 b) -1/2 + i(-1/2) c) square root of 3/2 + i(-1/2) d) -square root of 3/2 + i(-1/2)

Kirchoff's Laws : Mass-Spring Equation

Consider a basic electric circuit with a resistor, capacitor, and inductor and input voltage V(t). It follows Kirchoff's Laws that the charge on the capacitor Q = Q(t) solves the differential equation: {see attachment}, where L (inductance), R (resistance), and C (capacitance) are positive constants (depending on material). The

Quadratic Equations and Applications (Four Problems)

Assignment 5: Solutions of Quadratic Equations and their Applications 1. a) x2 + 6x + 7 = 0 b) z2 + z + 1=0 c) (3) ½ Y2 4y-7 (3) ½ = 0 d) 2x2 - 10x + 25 = 0 e) 2x2 +6x + 5 = 0 f) s2 - 4s + 4 = 0 g) 5/6x2 - 7x - 6/5 = 0 h) 7a2 +8a + 2 = 0 2. Given x = 1 and x = -8, form a quadratic equation. 3. What ty

Real, Rational and Complex Numbers

Please see the attached file for the fully formatted problems. 1. Classify the given numbers as real and rational, real and irrational, or complex. 2. a. Select any irrational number, and turn it into a rational number by using addition, subtraction, multiplication, division, or exponentiation. b. Select any imagina

How Do You Solve for u(x,t) using Separation of Variables?

Consider a model of a damped, oscillating string of length L, u_u = -2(lambda)(u_e) + (c^2)(u)_zz over 0 <= x <= L, where u(x, t) is the displacement, lambda describes the damping and c is the natural (undamped) wave speed. Suppose that the ends of the string are fixed at u = 0, and that the string is initially at rest, b

Complex Variables

If a > e prove that the equation a*z^n=e^z has n solutions (counting multiplicities) inside of the circle |z|=1.

Solve a complex variable equation.

Z is a complex number, s and t are real numbers. Find z1 and z2 - the solution the solutions of the equation. (z^2)+(|z|^2)-(2Is)=(8t^2) in terms of s and t. If z1*z2=-8I find s,t

Calc II

Find the open interval of convergence and test the endpoints for absolute and conditional convergence.

Matlab help for solving non-linear equations

[note: suggested number of credits may be modified if necessary] Hi, Part (1/2) I need help/advice in solving non-linear equations using Matlab. My focus is on the - Bisection method - Regula falsi - Muller's method (if possible) I have seen programs for the above methods on the internet, but I could not see *e

Help with an intro analysis proof

Due to the amount of symbols in the problem I attached a .pdf file. In words, I think the problem is asking - if the limit of f at c is positive, then on some deleted neighborhood of c, f is positive away from 0.

CLEP exam sample questions

Can you please help me with these. I can not get these and I am trying to study for the clep exam. Do not do the circled problems only the ones listed below. Thank you for help. Please show step so that I can understand better. 129 1. a) 6, b) 12, c) 16, d) 20 2. a) 24, b) 26 3. a) 35, b) 36 4. a) 46, b) 48 P. 14

Real Roots and Imaginary Roots

1. Find the number of real roots and imaginary roots: f(x)=10x^5-34x^4-5x^3-8x^2+3x+8 2. Find all zeros: f(x)=x^4+2x^3+5x^2+34x+30 3. Find all roots: f(x)=x^3-7x^2-17x-15; 2 + i 4. Find all roots: f(x)=x^4-6x^3+12x^2+6x-13; 3 + 2i The 5th problem is attached. Please answer the question

Cardinality for Irrational Numbers

1. Find the cardinality of the set of all irrational numbers, and prove your answer is correct. 2a. Is there a line in the x-y plane such that both coordinates of every point on the line are rational? Prove your answer is correct. 2b. Find the cardinality of the set of all complex numbers, and justify your answer. 3a. W

Complex Plane that are the Vertices of a Parallelogram

Find necessary and sufficient conditions (with proofs) such that the points z1, z2, z3, and z4 in the complex plane are the vertices of a parallelogram. I have read that the points z1, z2, z3, and z4 in the complex plane are vertices of a parallelogram if and only if z1 + z3 = z2 + z4. But, if this is indeed the case I would li

Understanding how to use the Queing Theory - Erlang M/G/s/GD/s/infinity.

How do I solve a formula or equation for the Erlang System M/G/s/GD/s/infinity that predicts resource requirements (how many servers) using the known variables (1) new events per unit of time; (2) average time per event; (3) event time service level (must be resolved by duration); (4) percent of events that must meet that event