unreality Posted January 15, 2008 Report Share Posted January 15, 2008 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) Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted January 16, 2008 Report Share Posted January 16, 2008 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. Quote Link to comment Share on other sites More sharing options...
0 unreality Posted January 16, 2008 Author Report Share Posted January 16, 2008 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. Quote Link to comment Share on other sites More sharing options...
0 roolstar Posted January 17, 2008 Report Share Posted January 17, 2008 no there's only one solution... Quote Link to comment Share on other sites More sharing options...
0 EventHorizon Posted January 17, 2008 Report Share Posted January 17, 2008 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... Quote Link to comment Share on other sites More sharing options...
0 roolstar Posted January 17, 2008 Report Share Posted January 17, 2008 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... Quote Link to comment Share on other sites More sharing options...
0 unreality Posted January 18, 2008 Author Report Share Posted January 18, 2008 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 EDIT: for some reason the square root symbol became a question mark, so I changed it from the square root symbol to 'v' Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted January 20, 2008 Report Share Posted January 20, 2008 Good one! I usually think of magnitude or modulus of complex numbers. But absolute value is used also. Quote Link to comment Share on other sites More sharing options...
0 unreality Posted January 21, 2008 Author Report Share Posted January 21, 2008 (okay pointless post, lol) Quote Link to comment Share on other sites More sharing options...
Question
unreality
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)
Link to comment
Share on other sites
8 answers to this question
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.