Complex Numbers and Harmonic

Related BrainMass Solutions

• Harmonic complex conjugates

  Complex Mathematics Problem GHD/CMATH-003 Complex valued function If f(z) = u + iv is analytic on a domain D, then u and v are both harmonic on D. Furthermore, if ux = vy and uy = -vx ,then v is said to be a harmonic conjugate of u.

• Complex Analysis Problem (analytic and harmonic functions)

  This solution goes through a complex analysis problem which pertains to analytic and harmonic functions.

• Complex Waveforms / Harmonic Distortion

  524223 Complex Waveforms / Harmonic Distortion Please find attached files for examples of Complex Waveform, Power Circuits and Harmonic Distortion, and Fourier Series.

• Kinetic and potential energy of harmonic oscillator, virial

  Calculate the energy expectation value and the kinetic energy expectation value K(t) = < | | > At any given time t, in terms of the constants cn. Show that your answers are real, even if the cn are complex. b.

• Cauchy-Riemann equations

  Show that f is constant. 2i) Verify that u=x2-y2-y is harmonic in the whole complex plane. 2ii) Suppose f(x,y)=u(x,y)+iv(x,y). The Cauchy-Riemann equation state that: ux=vy and uy=-vx.

• Fouriers analysis 'inverse' function.

  Question 1 Harmonic distortion is aserious problem for the electrical supply industry and can cause overheating of induction motors and transformers and cause the neutral conductor to carry more than its rated current Harmonic distortion is caused

• To find the analytic function f(z) = u + iv when u is given.

  + 4xy , then prove that u is a harmonic function and find the analytic function f(z) = u + iv .

• Harmonic Functions

  99897 Harmonic Functions A)Let a be less than b and set M(z)=(z-ia)/(z-ib). Define the lines L1={z:F(z)=b}, L2={z:F(z)=a} and L3={z:R(z)=0}. The three lines split the complex plane into 6 regions.

• Proving an Inequality : Let an, n>= 1 be an increasing sequence of positive real numbers. Prove that 1/a1 + 2/(a1 + a2) + .... + n/(a1 +... + an) < 4(1/a1 + 1/a2 + ... + 1/an)

  And if you see my proof, I have used the arithmetic-geometric-harmonic series to prove right side. However, the proof is indeed true and valid if 4 is replaced like: May be the 4 is the upper bound for the series.