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MATH / Let (a₁,b₁), (a₂,b₂), …, (a_(n),b_(n)) be all the ordered pairs (a,b) of complex numbers with a²+b²≠0, a+(10b)/(a²+b²)=5, and b+(10a)/(a²+b²)=4.Find a₁+b₁+a₂+b₂+…+a_(n)+b_(n).

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Let (a1,b1),(a_1,b_1), (a2,b2),(a_2,b_2), …,\dots, (an,bn)(a_n,b_n) be all the ordered pairs (a,b)(a,b) of complex numbers with a2+b2≠0,a^2+b^2\neq 0, a+10ba2+b2=5,andb+10aa2+b2=4.a+\frac{10b}{a^2+b^2}=5, \quad \text{and} \quad b+\frac{10a}{a^2+b^2}=4.Find a1+b1+a2+b2+…+an+bn.a_1 + b_1 + a_2 + b_2 + \dots + a_n + b_n.
Plain-text mathematical notation (without MathML)
Let (a₁,b₁), (a₂,b₂), …, (a_(n),b_(n)) be all the ordered pairs (a,b) of complex numbers with a²+b²≠0,
a+(10b)/(a²+b²)=5, and b+(10a)/(a²+b²)=4.Find a₁+b₁+a₂+b₂+…+a_(n)+b_(n).
Original LaTeX notation
Let $(a_1,b_1),$ $(a_2,b_2),$ $\dots,$ $(a_n,b_n)$ be all the ordered pairs $(a,b)$ of complex numbers with $a^2+b^2\neq 0,$
\[a+\frac{10b}{a^2+b^2}=5, \quad \text{and} \quad b+\frac{10a}{a^2+b^2}=4.\]Find $a_1 + b_1 + a_2 + b_2 + \dots + a_n + b_n.$

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
b0659a13-3e2f-597e-8e28-a8fbe8f14744
task_key
intermediate~5falgebra--test--b0659a13-3e2f-597e-8e28-a8fbe8f14744
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import