Maximize distance between complex expressions

2175ExpertComplex NumbersAlgebra

AIME II · 2012 · Problem 6

Let $z=a+bi$ be the complex number with $\vert z \vert = 5$ and $b > 0$ such that the distance between $(1+2i)z^3$ and $z^5$ is maximized, and let $z^4 = c+di$. Find $c+d$.

0 students attempted0% solvedRating 2175

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Maximize distance between complex expressions

2175ExpertComplex NumbersAlgebra

AIME II · 2012 · Problem 6

Let $z=a+bi$ be the complex number with $\vert z \vert = 5$ and $b > 0$ such that the distance between $(1+2i)z^3$ and $z^5$ is maximized, and let $z^4 = c+di$. Find $c+d$.

0 students attempted0% solvedRating 2175