MathDB
Complex is Real

Source: 2016 AIME I #7

March 4, 2016
2016 AIME IAIMEcomplex numbers

Problem Statement

For integers aa and bb consider the complex number ab+2016ab+100−(∣a+b∣ab+100)i.\dfrac{\sqrt{ab+2016}}{ab+100} - \left(\frac{\sqrt{|a+b|}}{ab+100}\right)i. Find the number of ordered pairs of integers (a,b)(a, b) such that this complex number is a real number.
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