Heat equation solving quadratic equation with complex numbers

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Homework Statement


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

Homework Equations


(-b±√b2-4ac)/2a
2-ρcpuλ-ρcpωi=0
λ=α+iβ±γ√(1+iδ)

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
 

Answers and Replies

  • #2
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6,386

Homework Statement


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

Homework Equations


(-b±√b2-4ac)/2a
2-ρcpuλ-ρcpωi=0
λ=α+iβ±γ√(1+iδ)

The Attempt at a Solution


so I plugged it in and came out with
(ρcpu/2k)±(ρcpu/2k)√1+(4kωi/ρcpu2)
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.

so γ=(ρcpu/2k) and δ=(4kω/ρcpu2)
but I'm unable to make the first term α+iβ and help would be great
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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