Use Your Imagination

Algebra Level 3

Which number is large?

3 i − 1 or 2 i 3i- 1 \quad \text{or} \quad 2i

3 i − 1 3i-1 This is not well-defined Both are equal 2 i 2i

Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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3 solutions

Inequalities are not well-defined in the complex plane, because it's not totally ordered. If the question was:

Which number is large?

∣ 2 i ∣ |2i| or ∣ 3 i − 1 ∣ |3i-1| the answer will be ∣ 3 i − 1 ∣ |3i-1| .

Thus the answer of this question is "Not well-defined"

3 Helpful 0 Interesting 0 Brilliant 0 Confused

By definition, no order relation exists among complex numbers. One can compare them only by taking their absolute values.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Which is where i got confused. By asking which is larger i assumed it meant 'which has a larger magnitude' since magnitude is informally referred to as 'size'. No?

Jeffrey Li - 5 years, 7 months ago

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Looks like no reference to 'size' has been given ! Yet, I do understand the confusion. Hope you overcame it.

Venkata Karthik Bandaru - 5 years, 7 months ago

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Yeah... never a good idea to make baseless assumptions, especially in a math question.

Jeffrey Li - 5 years, 7 months ago
Edwin Gray
Sep 11, 2018

Complex numbers cannot be ordered. Ed Gray

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