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
For an electric circuit, let V=cos 2pi(t) model the electromotive force in volts at t seconds. find smallest positive value of t where 0<and= to t<and= to 1/2 for the values a) V=0 b) V=.5 c) V=.25
Suppose P is a polynomial with real coefficients and P(a+bi)=0. Prove (a-bi)=0
Find all the complex cube roots of 2.
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
Solve the following equation. x^4 + 13x^2 + 36 = 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
Prove. Problem is attached in following file.
Show that if z0 is an nth root of unity(z0 is not equal to 1) then 1+z0+z0^2+...+z0^(n-1)=0. Hence show that cos(2Pi/1998)+cos(4Pi/1998)+...+cos(2Pi*1997/1998)=-1
Given u = y^3 - 3x^2y, find f(z) = u + iv such that f(z) is analytic. The solution is detailed and well presented.
Find the existence of a limit in a complex value function. Please see the attached file.
Given a function w = f(z) = z^2 then decompose f(z) into its real and imaginary parts.
Write the simplest polynomial equation that has roots 1+i and -1.
Solve (find the roots): (2x-3/x) + (5x-3/x^2) - (2x^2) + (x-6/x^3) = 2
Find the trigonometric form of the complex number where 0 <= theta < 2pi on the equation: r= 1/2 - [(sqrt(3)/2)i]
Find the roots. X^3 + 4*x^2 +6x -2 =0
Find all the zeros (both real and complex) of f(x)= x^5 - 3x^4 + 12x^3 - 28x^2 + 27x -9
1. Without solving the equation determine the number of roots (real, different, same, imaginary): a) 2x^2+7x-14=0 b) do the same for 2x^2-3x+10=0 c) e^2x+5=ln 125
What steps should be taken to solve complex order of operation equations?