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MATH / If w=cos40^(∘)+isin40^(∘), then

Problem

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problem

If w=cos40∘+isin40∘w=\cos40^\circ+i\sin40^\circ , then |w+2w2+3w3+…+9w9|−1|w+2w^2+3w^3+ \dots +9w^9|^{-1}can be expressed in the form absinn∘,\frac{a}{b} \sin n^\circ, where aa and bb are relatively prime positive integers, and nn is a positive integer smaller than 90. Find a+b+n.a + b + n.
Plain-text mathematical notation (without MathML)
If w=cos40^(∘)+isin40^(∘), then
|w+2w²+3w³+…+9w⁹|^(−1)can be expressed in the form (a)/(b)sinn^(∘), where a and b are relatively prime positive integers, and n is a positive integer smaller than 90.  Find a+b+n.
Original LaTeX notation
If $w=\cos40^\circ+i\sin40^\circ $, then
\[|w+2w^2+3w^3+ \dots +9w^9|^{-1}\]can be expressed in the form $\frac{a}{b} \sin n^\circ,$ where $a$ and $b$ are relatively prime positive integers, and $n$ is a positive integer smaller than 90.  Find $a + b + n.$

level

Level 4

type

Precalculus

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Source and history

task_id
64952667-46a4-5682-acde-690dcb1470db
task_key
precalculus--test--64952667-46a4-5682-acde-690dcb1470db
task_revision_id
1
config / split
precalculus / test

Official source

initial import