MathDB

Complex Number Combo

Source: 2022 AIME I #4

February 9, 2022

AMCAIMEAIME Icomplex numbers

Problem Statement

Let

w = \frac{\sqrt{3}+i}{2}

and

z=\frac{-1+i\sqrt{3}}{2}

, where

i=\sqrt{-1}

. Find the number of ordered pairs

(r, s)

of positive integers not exceeding

100

that satisfy the equation

i\cdot w^r=z^s

.

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