## heat equation solving quadratic equation with complex numbers

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
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Mentor
 Quote by dp182 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 kλ2-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)
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.

 Quote by dp182 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.

 Tags complex numbers, heat equation, quadratic equation, substitution