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November 2nd, 2010, 10:56 AM   #1
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Complex numbers question

Which complex numbers satisfy:

?

Attempt:







I am not sure what else there is to do
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November 2nd, 2010, 01:07 PM   #2
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Re: Complex numbers question

Actually, you know that is a real number. Thus, z must be a real number.

When does whenever x is a real number?
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November 3rd, 2010, 07:15 AM   #3
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Re: Complex numbers question

Quote:
Originally Posted by six
Actually, you know that is a real number. Thus, z must be a real number.

When does whenever x is a real number?
Well x would always equal |x|, since
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November 3rd, 2010, 10:27 AM   #4
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Re: Complex numbers question

-1 =\= |-1|
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November 3rd, 2010, 12:11 PM   #5
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Re: Complex numbers question

See, the problem is that x^2 doesn't have an inverse! The sqrt is not a function (do you see why?).
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November 6th, 2010, 01:09 AM   #6
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Re: Complex numbers question

Quote:
Originally Posted by six
See, the problem is that x^2 doesn't have an inverse! The sqrt is not a function (do you see why?).
Cause a square root returns 2 values (+ and -)?
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November 6th, 2010, 03:44 AM   #7
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Re: Complex numbers question

Precisely.

In case you're wondering though, represents positive values only, since it doesn't have a plus or minus sign in front of it.
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November 16th, 2010, 05:27 PM   #8
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Re: Complex numbers question

Six, do you know what sqrt is?
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November 16th, 2010, 06:49 PM   #9
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Re: Complex numbers question

Could you please elaborate instead of asking a silly question? Just tell me what's wrong with my reasoning instead, please.
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November 16th, 2010, 07:55 PM   #10
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Re: Complex numbers question

Sqrt is certainly a function. It is defined to be the inverse of restricted to . When solving quadratic equations you must use a plus and minus sqrt , but sqrt as a function has nothing to do with +/-
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