heat equation solving quadratic equation with complex numbers

dp182

1. The problem statement, all variables and given/known data
given that kλ²-ρc_puλ-ρc_pωi=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±√b²-4ac)/2a
kλ²-ρc_puλ-ρc_pωi=0
λ=α+iβ±γ√(1+iδ)
3. The attempt at a solution
so I plugged it in and came out with
(ρc_pu/2k)±(ρc_pu/2k)√1+(4kωi/ρc_pu²)
so γ=(ρc_pu/2k) and δ=(4kω/ρc_pu²)
but I'm unable to make the first term α+iβ and help would be great

Mark44

Should be λ= (ρc_pu/2k)±(ρc_pu/2k)√1+(4kωi/ρc_pu²) 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 = ρc_pu/(2k) and β = 0.