Turn on thread page Beta

    i = sqr(-1)

    i = sqr ( 1 / -1 )

    i = sqr 1 / sqr (-1) = +- (1 / i)

    with - gives: i = i, ok

    with + gives i = -i ?????????

    Ï "Sekhmet" <[email protected]> Ýãñáøå óôï ìÞíõìá news:[email protected]...
    [q1]> i = sqr(-1)[/q1]
    [q1]>[/q1]
    [q1]> i = sqr ( 1 / -1 )[/q1]
    [q1]>[/q1]
    [q1]> i = sqr 1 / sqr (-1) = +- (1 / i)[/q1]
    [q1]>[/q1]
    [q1]> with - gives: i = i, ok[/q1]
    [q1]>[/q1]
    [q1]> with + gives i = -i ?????????[/q1]
    [q1]>[/q1]
    [q1]>[/q1]

    You make error, because

    i=sqr(1)/sqr(-1)=1/i ==> (sqr(1)=1 and sqr(-1)=i) i=1/i==>i^2=1

    tilemachos

    "Sekhmet" <[email protected]> wrote:
    [q1]> i = sqr(-1)[/q1]
    [q1]>[/q1]
    [q1]> i = sqr ( 1 / -1 )[/q1]
    [q1]>[/q1]
    [q1]> i = sqr 1 / sqr (-1) = +- (1 / i)[/q1]
    [q1]>[/q1]
    [q1]> with - gives: i = i, ok[/q1]
    [q1]>[/q1]
    [q1]> with + gives i = -i ?????????[/q1]

    I'm slightly surprised that there hasn't yet been a response showing where the error lies, so I'll
    try to do so now.

    There are two different approaches.

    (1) If your "sqr" is used to denote the _principal_ square root, as your first line seems
    to indicate:

    Let me now denote it as Sqrt instead. Then i = Sqrt(-1) = Sqrt(1/(-1)) is correct, and
    Sqrt(1)/Sqrt(-1) = 1/i = -i is also correct [and, BTW, Sqrt(1)/Sqrt(-1) = -(1/i) = +i is
    incorrect]. So the error lies in claiming that Sqrt(1/(-1)) = Sqrt(1)/Sqrt(-1). The "law" that
    Sqrt(a/b) = Sqrt(a)/Sqrt(b) does not always hold! [Note, however, that it does hold if both a and
    b are positive.]

    (2) If your "sqr" is used to denote the _set_ of _all_ squares roots, as the end of your third line
    seems to indicate:

    Let me now denote it as sqrt instead. Then the left side of each of your lines should read +/-i,
    as an abbreviation for {-i, +i}. Then the law sqrt(a/b) = sqrt(a)/sqrt(b) _does_ hold.
    Specifically, we have +/-i = sqrt(-1) = sqrt(1/(-1)) = sqrt(1)/sqrt(-1) = (+/-1)/(+/-i) = +/-i. No
    contradiction.

    David Cantrell

    --
    -------------------- http://NewsReader.Com/ -------------------- Usenet Newsgroup Service
 
 
 
Turn on thread page Beta
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

Updated: May 20, 2002
Poll
Black Friday: Yay or Nay?
Useful resources

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.