# Complex number inequality question

• B
• bonbon22
So for |z|<2 we have a disk of radius 2, centered at the origin.In summary, the modulus of a complex number z is the distance from the origin to the point (x, y) in the complex plane. If |z| < 2, then z is located within a disk of radius 2 centered at the origin. This is because the modulus of a complex number is defined as the square root of the product of the number and its complex conjugate, which results in a distance that is always positive. However, the inequality |z| < 2 does not represent a circle, but rather a disk.
bonbon22
TL;DR Summary
[z]<2 is a circle but im still not too sure why.
Z can be any point on the argand diagram so if z molous is less than 2 , is that somehow giving us the distance from origin? But how i assumed mod sign only makes things positive therefore its not sqrt( (x+yi)^2 ) = distance ??

bonbon22 said:
Summary: [z]<2 is a circle but I am still not too sure why.

Z can be any point on the argand diagram so if z molous is less than 2 , is that somehow giving us the distance from origin? But how i assumed mod sign only makes things positive therefore its not sqrt( (x+yi)^2 ) = distance ??

The modulus of a complex number ##z## is defined as ##|z| = \sqrt{zz^*} = \sqrt{x^2 +y^2}##

bonbon22 said:
molous
You're missing a 'd'. The word is modulus.
For a complex number z, |z| is the distance from the origin to the point (x, y) in the complex plane.

It's not a circle. Notice a circle is described by |z|=c , c a constant. You have an < instead.

Delta2
To elaborate on @WWGD's correction, the inequality ##|z| < c##, with c a nonnegative real constant, is a disk. The boundary of a disk is a circle.

Delta2

## 1. What is a complex number inequality?

A complex number inequality is an inequality that involves complex numbers, which are numbers that have both a real and imaginary component. These inequalities can be expressed in terms of greater than, less than, or equal to, and can involve both real and imaginary parts of the complex numbers.

## 2. How do you solve a complex number inequality?

To solve a complex number inequality, you can follow the same steps as solving a regular inequality. First, you need to isolate the variable on one side of the inequality. Then, you can use the properties of complex numbers to manipulate the inequality and find the solution set. Finally, you can graph the solution set on the complex plane to visualize the solution.

## 3. Can a complex number be greater than or less than another complex number?

Yes, complex numbers can be compared using the greater than and less than symbols. This is because complex numbers have both a real and imaginary part, which can be compared separately. For example, if two complex numbers have the same real part, the one with the larger imaginary part would be considered greater.

## 4. Are there any special properties of complex number inequalities?

Yes, there are a few special properties of complex number inequalities. One is the triangle inequality, which states that the absolute value of the sum of two complex numbers is less than or equal to the sum of the absolute values of the individual complex numbers. Another property is that multiplying or dividing both sides of a complex number inequality by a positive real number will not change the inequality, but multiplying or dividing by a negative real number will reverse the inequality sign.

## 5. How are complex number inequalities used in real life?

Complex number inequalities have various applications in fields such as physics, engineering, and economics. They can be used to model and solve problems involving alternating currents, electric circuits, and financial investments. They are also used in signal processing and control systems to analyze and optimize performance. In addition, complex number inequalities are used in computer graphics to create 3D images and animations.

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