Dick said:No, |z+w| is NOT equal to |z-w|. Your first inequality is true for all w. Therefore it also must be true for -w. Substitute '-w' everywhere you see 'w' in the first inequality.
The inequality of complex numbers is a mathematical concept that compares the magnitudes of two complex numbers. It is determined by calculating the distance between the two numbers on a complex plane.
The inequality of complex numbers is represented using the absolute value or modulus notation, denoted by |z|, where z is a complex number. This notation indicates the distance of the complex number from the origin on the complex plane.
To solve this inequality, you need to use the properties of absolute value and the Pythagorean theorem. First, expand the equation to get |z+w|^2 = |z-w|^2. Then, use the Pythagorean theorem to simplify the equation and solve for the values of z and w.
The inequality |z+w|=|z-w| represents a pair of points on the complex plane that are equidistant from the origin. This creates a line that bisects the complex plane, dividing it into two regions.
Understanding the inequality of complex numbers is important because it allows us to compare and contrast the magnitudes of complex numbers. This concept is essential in various fields, such as physics, engineering, and economics, where complex numbers are used to represent real-world phenomena.