### 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)

Explore BrainMass

- Anthropology
- Art, Music, and Creative Writing
- Biology
- Business
- Chemistry
- Computer Science
- Drama, Film, and Mass Communication
- Earth Sciences
- Economics
- Education
- Engineering
- English Language and Literature
- Gender Studies
- Health Sciences
- History
- International Development
- Languages
- Law
- Mathematics
- Philosophy
- Physics
- Political Science
- Psychology
- Religious Studies
- Social Work
- Sociology
- Statistics

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. 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)

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

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

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

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

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

Functions of a Complex Variables Analytic Functions If u = sin x . cosh y + 2cos x . sinh y + x2 - y2 + 4xy , then prove that u is a harmonic function and find the analytic funct

Functions of a Complex Variables ∞ ∞ Prove that │∑ zn │ ≤ ∑│zn │ where zn is a complex number. n =1 n =1

Please answer the attached complex variable problems. Thank you.

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

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

[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

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.

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

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

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

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

If v is a signed measure, E is v-null if |v|(E)=0

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

Write the simplest polynomial equation that has roots 1+i and -1.

What steps should be taken to solve complex order of operation equations?