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 ??
You're missing a 'd'. The word is modulus.bonbon22 said:molous
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.
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.
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.
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.
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.