(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

given that kλ^{2}-ρc_{p}uλ-ρc_{p}ωi=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,c_{p},u,k, and ω

2. Relevant equations

(-b±√b^{2}-4ac)/2a

kλ^{2}-ρc_{p}uλ-ρc_{p}ωi=0

λ=α+iβ±γ√(1+iδ)

3. The attempt at a solution

so I plugged it in and came out with

(ρc_{p}u/2k)±(ρc_{p}u/2k)√1+(4kωi/ρc_{p}u^{2})

so γ=(ρc_{p}u/2k) and δ=(4kω/ρc_{p}u^{2})

but I'm unable to make the first term α+iβ and help would be great

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# Heat equation solving quadratic equation with complex numbers

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