# 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.

## Homework Statement

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

N/A

## The Attempt at a Solution

[PLAIN]http://img530.imageshack.us/img530/1786/aaakr.jpg
Both of them have a moduli of 5.
So should the circle centred at the origin or at (-3,4i)?

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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..

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.

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|"

The question says if z = -3+4i, determine |z| and use complex plane diagrams to illustrate their relationship with the original complex number.
thanks!

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.

## 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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