# Complex Analysis Graphing Question

• kathrynag
In summary, the conversation is about proving the equation z1+(z2+z3)=(z1+z2)+z3 using a graph. The concept of representing complex numbers as vectors in the Argand Plane is discussed, and it is suggested to add the vectors in different orders to show that they result in the same point. The person asking the question confirms their understanding and clarifies the process of adding the vectors.
kathrynag

## Homework Statement

I want to show $$z_{1}$$+($$z_{2}$$+$$z_{3}$$)=($$z_{1}$$+$$z_{2}$$)+$$z_{3}$$ with the use of a graph.

## The Attempt at a Solution

I am just cluless on how to graph. I know z=x+iy where the real part is on the x-axis and the imaginary part is on the y axis.

Well, each complex number can be represented by a vector in the Argand Plane. You should know how to add vectors, if not its easy to learn and is probably in your textbook. Basically it's just a matter of adding two of the vectors first, then the last, and showing that lands you in the same place as adding another pair, then the last. Ie Order doesn't matter.

ok, I think I understand. So, I have z1 and z2 and show what happens when I add z3 to it?

Each of them is a vector,

Did you draw z_1, then z_2 + z_3, now what happens when you add those 2 together?

Now what happens when you draw z_1 + z_2 and then add z_3 to it?

## 1. What is complex analysis?

Complex analysis is a branch of mathematics that deals with the study of functions of complex numbers. It involves the analysis of functions that map complex numbers to other complex numbers.

## 2. What is a complex graph?

A complex graph is a visual representation of a function or equation that involves complex numbers. It typically consists of two axes, one for the real part and one for the imaginary part, and plots the values of the function at various points on the complex plane.

## 3. How do I plot a complex graph?

To plot a complex graph, you will need to understand the properties of complex numbers and how they are represented on the complex plane. You will also need to use software or a graphing calculator that is capable of plotting complex functions.

## 4. What are some common complex functions?

Some common complex functions include polynomials, exponential functions, logarithmic functions, and trigonometric functions. These functions can have complex inputs and outputs, making them suitable for graphing in the complex plane.

## 5. What are some real-life applications of complex analysis and graphing?

Complex analysis and graphing have many real-life applications, such as in physics, engineering, and economics. They are used to model and analyze complex systems and phenomena, such as electrical circuits, fluid dynamics, and stock market trends.

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