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MATH / Let w and z be complex numbers such that |w|=1 and |z|=10. Let theta = arg left(frac{w-z}{z}right). Find the maximum possible value of tan²θ. (Note that arg(w), for w≠0, denotes th…

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problem

Let ww and zz be complex numbers such that |w|=1|w| = 1 and |z|=10|z| = 10. Let $\theta = \arg \left(\frac{w-z}{z}\right)$. Find the maximum possible value of tan2θ.\tan^2 \theta. (Note that $\arg(w),$ for w≠0,w \neq 0, denotes the measure of the angle that the ray from 0 to ww makes with the positive real axis in the complex plane.)
Plain-text mathematical notation (without MathML)
Let w and z be complex numbers such that |w|=1 and |z|=10. Let $\theta = \arg \left(\frac{w-z}{z}\right)$. Find the maximum possible value of tan²θ.  (Note that $\arg(w),$ for w≠0, denotes the measure of the angle that the ray from 0 to w makes with the positive real axis in the complex plane.)
Original LaTeX notation
Let $w$ and $z$ be complex numbers such that $|w| = 1$ and $|z| = 10$. Let $\theta = \arg \left(\frac{w-z}{z}\right)$. Find the maximum possible value of $\tan^2 \theta.$  (Note that $\arg(w),$ for $w \neq 0,$ denotes the measure of the angle that the ray from 0 to $w$ makes with the positive real axis in the complex plane.)

level

Level 3

type

Precalculus

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Source and history

task_id
456b066e-ae97-54bc-87fc-96fad8a0a310
task_key
precalculus--test--456b066e-ae97-54bc-87fc-96fad8a0a310
task_revision_id
1
config / split
precalculus / test

Official source

initial import