MathDB
Complex Number

Source: 1994 National High School Mathematics League, Exam Two, Problem 1

March 2, 2020
complex numbers

Problem Statement

In the equation x2+z1x+z2+m=0x^2+z_1x+z_2+m=0, z1,z2,mz_1,z_2,m are complex numbers, and z12−4z2=16+20iz_1^2-4z_2=16+20\text{i}. Two roots of the equations are α,β\alpha,\beta. If ∣α−β∣=27|\alpha-\beta|=2\sqrt7, find the maximum and minumum value of ∣m∣|m|.
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