A basic question about complex numbers

In summary, the conversation discusses the definition of modulus for complex numbers and clarifies a misconception about its calculation. The correct formula for calculating modulus is explained, and it is noted that the modulus can also be found by taking the square root of the complex number multiplied by its conjugate.
  • #1
qazxsw11111
95
0
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+ 31/2i)l = ((-1)2+(30.5)2)1/2

But according to my understanding, isn't 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.
 
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  • #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.
 
  • #3
Yes! Thank you! Yeah, I was just reading my textbook and didnt really memorize the formula correctly.
 
  • #4
qazxsw11111 said:
Yes! Thank you! Yeah, I was just reading my textbook and didnt really memorize the formula correctly.

np, good luck :-D
 
  • #5
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?

chota said:
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
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.
 

1. What are complex numbers?

Complex numbers are numbers that are expressed in the form of a + bi, where a and b are real numbers and i is the imaginary unit, defined as the square root of -1.

2. How are complex numbers represented in the complex plane?

In the complex plane, the real part of a complex number, a, is represented on the horizontal axis and the imaginary part, bi, is represented on the vertical axis. The point where the two axes intersect is the origin, and the distance from the origin to the point representing the complex number is its magnitude.

3. What are the operations that can be performed on complex numbers?

Complex numbers can be added, subtracted, multiplied, and divided, just like real numbers. Additionally, they can be raised to a power or have roots taken.

4. What is the conjugate of a complex number?

The conjugate of a complex number a + bi is denoted as a - bi. It has the same real part as the original complex number, but the sign of the imaginary part is flipped.

5. How are complex numbers used in real life?

Complex numbers have many applications in mathematics, physics, and engineering. They are used to model and analyze alternating currents, oscillations, and other complex systems. They also have practical uses in computer graphics, signal processing, and cryptography.

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