# A basic question about complex numbers

1. Oct 19, 2008

### qazxsw11111

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.

2. Oct 19, 2008

### chota

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. Oct 19, 2008

### qazxsw11111

Yes! Thank you! Yeah, I was just reading my textbook and didnt really memorize the formula correctly.

4. Oct 19, 2008

### chota

np, good luck :-D

5. Oct 20, 2008

### KRiBaH

What do you mean?

Isn't much easier to make a sqrt of (-1)2+(31/2)2i?

Last edited: Oct 20, 2008
6. Oct 20, 2008

### HallsofIvy

Staff Emeritus
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.