A basic question about complex numbers

[qazxsw11111]

Hi. I have recently scratched the basics of complex numbers and just learned the modulus. I looked at one of the examples on my textbook which states that

l (-1+ 3^1/2i)l = ((-1)²+(3^0.5)²)^1/2

But according to my understanding, isn't the l3^1/2il 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.

 

[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.

 

[qazxsw11111]

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

 

[chota]

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

np, good luck :-D

 

[KRiBaH]

isnt the l3^1/2il 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+(3^1/2)²i?

 

[HallsofIvy]

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.