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2010 Calculus #7: Minimization of Multivariable Expression

Source:

July 15, 2012
calculusinequalitiescomplex numbers

Problem Statement

Let a1a_1, a2a_2, and a3a_3 be nonzero complex numbers with non-negative real and imaginary parts. Find the minimum possible value of ∣a1+a2+a3∣∣a1a2a3∣3.\dfrac{|a_1+a_2+a_3|}{\sqrt[3]{|a_1a_2a_3|}}.
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