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Heat equation solving quadratic equation with complex numbers

  1. Nov 1, 2011 #1
    1. The problem statement, all variables and given/known data
    given that kλ2-ρcpuλ-ρcpωi=0
    plug into the quadratic formula and get out an equation that looks like this

    λ=α+iβ±γ√(1+iδ) where α,β,γ,and δ are in terms of ρ,cp,u,k, and ω

    2. Relevant equations
    (-b±√b2-4ac)/2a
    2-ρcpuλ-ρcpωi=0
    λ=α+iβ±γ√(1+iδ)
    3. The attempt at a solution
    so I plugged it in and came out with
    (ρcpu/2k)±(ρcpu/2k)√1+(4kωi/ρcpu2)
    so γ=(ρcpu/2k) and δ=(4kω/ρcpu2)
    but I'm unable to make the first term α+iβ and help would be great
     
  2. jcsd
  3. Nov 1, 2011 #2

    Mark44

    Staff: Mentor

    Should be λ= (ρcpu/2k)±(ρcpu/2k)√1+(4kωi/ρcpu2) since you are solving the quadratic equation for λ. Note that I didn't check your work.

    They're not asking you to make the first term α+iβ, just that you have an equation that has the form they give. In what you have, α = ρcpu/(2k) and β = 0.
     
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