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I am thinking of a number.

It's absolute value is √29

but if you add 2 to the number...

it's absolute value is √53!

What is the number? (there is only one answer)

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Posted · Report post

I am thinking of a number.

It's absolute value is √29

but if you add 2 to the number...

it's absolute value is √53!

What is the number? (there is only one answer)

Is that the correct interpretation?

SQRT[29] = ABOUT 5.38

SQRT[53] = ABOUT 7.28

These differ by 1.9, which is ABOUT equal to 2.

But that can't be it ... right?

I take "absolute value" to mean drop the MINUS SIGN if there is one.

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bonanova the answer spoiler is wrong (wow I thought I'd never ever ever ever ever say that...lol)... the answer is EXACTLY 2

and I use the usual definition of absolute value: DISTANCE FROM ZERO

and I was wrong- there are actually 2 solutions. Name them both. :P

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Posted · Report post

no there's only one solution...

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I am thinking of a number.

It's absolute value is √29

but if you add 2 to the number...

it's absolute value is √53!

What is the number? (there is only one answer)

5±2i, but people that haven't worked much with complex numbers wouldn't have a clue...

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Posted · Report post

5±2i, but people that haven't worked much with complex numbers wouldn't have a clue...

Actually 5 + 2i does not work:

(5 + 2i)2 = 25 -4 = 21

So only one solution...

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This is the solution:

EventHorizon is right, it's 5±2i, though I consider that two different answers (5+2i and 5-2i)

absolute value of 5+2i = v(25+4) = v29

absolute value of 5-2i = v(25+4) = v29

roolstar, remember that absolute value is defined (at least for this problem) as distance from zero. We're not actually squaring the 'i' part, cuz if we were, 2i squared would of course be -4, but we're not squaring the 'i' part, just the -2/+2 part because that's the distance from zero for the 'i' part of the complex number, which is thus 4 either way.

In other words, we're dealing with two axes of a graph here, and lets say 'r' stands for real and 'i' stands for imaginary: 5r+2i. The 'r' and the 'i' are just like 'y' or 'x'. They don't affect the distance from zero

when 2 is added, the equation becomes 7±2i, whose abs value is sqr root 53

EventHorizon was correct :D

EDIT: for some reason the square root symbol became a question mark, so I changed it from the square root symbol to 'v'

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Posted · Report post

Good one!

I usually think of magnitude or modulus of complex numbers.

But absolute value is used also.

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Posted · Report post

:D (okay pointless post, lol)
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