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 Problem: For , Prove that n = 1 if and only if 3 | n, for any integer n.
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?