A basic question about complex numbers

  • #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.
 

Answers and Replies

  • #2
22
0
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.
 
  • #3
Yes! Thank you! Yeah, I was just reading my textbook and didnt really memorize the formula correctly.
 
  • #4
22
0
Yes! Thank you! Yeah, I was just reading my textbook and didnt really memorize the formula correctly.

np, good luck :-D
 
  • #5
3
0
qazxsw11111;1921526 [I said:
isnt the l31/2il supposed to be sqrt of 3i2, in which it is a 3(-1). [/I]

What do you mean?

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.

Isn't much easier to make a sqrt of (-1)2+(31/2)2i?
 
Last edited:
  • #6
HallsofIvy
Science Advisor
Homework Helper
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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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