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A basic question about complex numbers

  1. Oct 19, 2008 #1
    Hi. I have recently scratched the basics of complex numbers and just learnt the modulus. I looked at one of the examples on my textbook which states that

    l (-1+ 31/2i)l = ((-1)2+(30.5)2)1/2

    But according to my understanding, isnt the l31/2il supposed to be sqrt of 3i2, in which it is a 3(-1). But typing the equation into my graphic calcuator reveals the results as shown on the textbook, meaning my understanding is wrong.

    Any helps please? Thanks.
  2. jcsd
  3. Oct 19, 2008 #2
    THe definition of modulus for any complex number z = x+iy is (x^2 + y^2 ) ^ 1/2

    so for your example, if z = -1 + i*(3)^1/2
    then the modulus of z would be ((-1)^2 + ( (3)^1/2) ^2 ) ^ 1/2 which is just
    (1 + 3) ^ 1/2 = 4^1/2 = 2

    Hope this helps.

    Maybe you are reading or wrote down the wrong definition for modulus.
  4. Oct 19, 2008 #3
    Yes! Thank you! Yeah, I was just reading my textbook and didnt really memorize the formula correctly.
  5. Oct 19, 2008 #4
    np, good luck :-D
  6. Oct 20, 2008 #5
    What do you mean?

    Isn't much easier to make a sqrt of (-1)2+(31/2)2i?
    Last edited: Oct 20, 2008
  7. Oct 20, 2008 #6


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    It is also helpful to remember that |z| is the square root if z times its complex conjugate. If z= x+ iy, then it's conjugate is x- iy: (x+ iy)(x- iy)= x2- (iy)2= x2-(-y2)= x2+ y2.
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