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Prove $|(a+bi)^n| = |(a+bi)|^n$

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#complex-numbers #absolute-value
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Find the sum of values of $x$ that satisfies $\left | 3x-3 \right | + \left | 4x-4 \right | + \left | 5x-5 \right | \geq 24$

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#inequality #absolute-value
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Absolute value of a square root

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#absolute-value
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Proof of this property: $x=0$ if and only if $|x|<z$ for all $z>0$

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#inequality #proof-verification #absolute-value #alternative-proof
49
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Triangular inequality - sum of the absolutes and absolut of the sum

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#inequality #summation #absolute-value
83
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Can the order of absolute value and limit be swapped?

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#real-analysis #limits #convergence-divergence #normed-spaces #absolute-value
241
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Complex Numbers Inequality from GM

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#inequality #complex-numbers #contest-math #absolute-value
421
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Differentiating mean absolute error

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#calculus #expectation #partial-derivative #absolute-value
64
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Why these conclusions from the definition? Absolute value

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#algebra-precalculus #definition #absolute-value
185
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Do all fields with internal absolute values arise either as ordered fields or like $\mathbb{C}$ from them?

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#abstract-algebra #absolute-value #ordered-fields
70
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Boundedness of a real-valued sequence

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#real-analysis #sequences-and-series #absolute-value
100
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Prove that the roots of a given polynomial don't have the same absolute value

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#polynomials #roots #absolute-value
236
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Prove the $x\leq \lvert x \rvert$ (absolute value)

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#calculus #proof-verification #definition #absolute-value
76
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Absolute value of real numbers and inequality

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#inequality #absolute-value
1.6k
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How to solve this logarithm inequality with absolute value as its base?

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#algebra-precalculus #inequality #logarithms #absolute-value

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