HELP Absolute Values on a Complex Plane

In summary, the question asks to determine the absolute value or magnitude, |z|, of the complex number z = -3+4i and then illustrate its relationship with the original complex number by graphing it on a complex plane diagram. The absolute value or magnitude of z is determined by finding its distance from the origin, which in this case is 5 units to the right of the origin on the real axis. This can be represented by a single point on the real axis, with no need for a circle. However, if we were to graph all possible values of z such that |z| = |-3+4i|, we would get a circle centered at the origin with a radius of 5.
  • #1
wadahel
3
0

Homework Statement


Draw |z| on a complex plane, where z = -3+4i


Homework Equations


N/A


The Attempt at a Solution


[PLAIN]http://img530.imageshack.us/img530/1786/aaakr.jpg
Can anyone please tell me which answer is correct?
Both of them have a moduli of 5.
So should the circle centred at the origin or at (-3,4i)?
 
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  • #2
are you trying to draw |z|=5 ? in that case, your first graph is correct since origin should lie
on the circle because the distance between the origin and (-3,4i) is 5..
 
  • #3
IssacNewton said:
are you trying to draw |z|=5 ? in that case, your first graph is correct since origin should lie
on the circle because the distance between the origin and (-3,4i) is 5..
The OP doesn't say anything about graphing |z| = 5, just |z|.

If z = -3 + 4i, then |z| = 5. This would be a single point on the Re axis 5 units to the right of the origin.
 
  • #4
I suspect that wadahel has misunderstood the question. Graphing the number "5" on the complex plane doesn't make a lot of sense. wadahel, what was the exact wording of the problem? Are you go graph "|z| where z= -3+ 4i" or "graph all z such that |z|= |-3+ 4i|"
 
  • #5
The question says if z = -3+4i, determine |z| and use complex plane diagrams to illustrate their relationship with the original complex number.
thanks!
 
  • #6
That still doesn't make a lot of sense. In this case |z| = 5. "... illustrate their relationship ..." "Their" implies two or more things, but here you have only one thing: |z|.

About the only relationship I can think of is that -3 + 4i determines one vertex in a right triangle, and 5 is the length of the hypotenuse of that triangle.
 

Related to HELP Absolute Values on a Complex Plane

1. What are absolute values on a complex plane?

Absolute values on a complex plane refer to the distance of a complex number from the origin (0,0) on a two-dimensional graph. It is represented by the modulus symbol (|z|) and is always a positive real number.

2. How are absolute values calculated on a complex plane?

The absolute value of a complex number is calculated by taking the square root of the sum of the squares of its real and imaginary parts. In other words, |z| = √(x^2 + y^2), where z = x + yi.

3. What is the significance of absolute values on a complex plane?

Absolute values on a complex plane are important in determining the magnitude or size of a complex number. It is also useful in finding the distance between two points on a complex plane, as well as in solving complex equations and performing operations on complex numbers.

4. How are absolute values represented visually on a complex plane?

On a complex plane, absolute values are represented by the distance of a point from the origin. This distance can be measured using a ruler or by counting the grid lines on the graph. The further away the point is from the origin, the larger its absolute value.

5. Can absolute values be negative on a complex plane?

No, absolute values on a complex plane are always positive. This is because the distance from a point to the origin cannot be negative. Therefore, the absolute value of any complex number will always be a positive real number.

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