If z is a non-real complex number, then the minimum value of Imz5/(Imz)5 is

zis a non-real complex number.letz=reiθImz5(Imz)5=r5sin5θr5sin5θsay,f(θ)=sin5θsin5θequating first derivative to0f′(θ)=0⇒sin5θ⋅5cos5θ−sin5θ⋅5sin4θ⋅cosθ⇒sinθ⋅cos5θ=cosθ⋅sin5θ⇒tanθ=tan5θ⇒θ=0,π/4...butf(0)is indeterminatef(π/4)=𕒸∴Minimum value ofImz5(Imz)5is𕒸Hence, optionB.