Modulus of a Complex Number Question

In summary, the conversation discusses the concept of modulus of a complex number and how it differs from the absolute value. The problem at hand is to graph the set of points satisfying the equation |z-1+i|=1. One person suggests that the graph would only have two points, but another points out that this is incorrect and explains how to correctly solve the equation using the modulus formula. The conversation ends with the correct solution being identified as a circle.
  • #1
tylerc1991
166
0

Homework Statement



My prof was saying today that the modulus of a complex number isn't the absolute value. The problem is the following:

Graph the set of points satisfying the following equation(s):

|z-1+i|=1

The Attempt at a Solution



Can I not just say that z = -i or z = 2-i and hence the graph is just two points? Or is this the correct answer?
 
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  • #2
If you plot |z-1+i|=1 on an argand digram, you will see that this does not give only two solutions. If you put z=x+iy into the equation and then find the modulus knowing that |a+ib|=√(a2+b2), what do you get?
 
  • #3
I see what I did wrong now. If I let z = x + iy I am getting:

(x-1)^2 + (y+1)^2 = 1, which is obviously a circle.

Thanks!
 

Related to Modulus of a Complex Number Question

1. What is the modulus of a complex number?

The modulus of a complex number is its distance from the origin on the complex plane. It is also known as its magnitude or absolute value.

2. How do you calculate the modulus of a complex number?

To calculate the modulus of a complex number, you take the square root of the sum of the squares of its real and imaginary parts. In other words, if a + bi is a complex number, the modulus is equal to √(a² + b²).

3. Why is the modulus of a complex number important?

The modulus of a complex number is important because it gives us information about the magnitude and direction of the number on the complex plane. It is also used in various mathematical and scientific calculations involving complex numbers.

4. Can the modulus of a complex number be negative?

No, the modulus of a complex number cannot be negative. It is always a positive value or zero.

5. How is the modulus of a complex number related to its conjugate?

The modulus of a complex number is equal to the modulus of its conjugate. This means that the distance from the origin to a complex number is the same as the distance from the origin to its conjugate. It also means that the magnitude of a complex number is unchanged when its sign is flipped.

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