The absolute value of a number is often viewed as the "distance" a number is away from 0, the origin.
For real numbers, the absolute value is just the magnitude of the number without considering its sign. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5.
For a complex number represented on the complex plane by the pair , the "distance" from the origin is found using the Pythagorean theorem. The absolute value of is defined as
For example, the absolute value of the complex number is equal to
The absolute value can also be written as
where is the complex conjugate of
What is the absolute value of the complex number
The absolute value of the complex number is What is the negative number
The absolute value of is implying or This implies Since is negative,
The absolute value of the complex number can be expressed as where and are real numbers and is the imaginary number. What are and
Observe that the absolute value of a complex number can be written as where is the complex conjugate of Then since thus which implies that and
What is the absolute value of the following sum of complex numbers:
Let be the coordinates of the complex number on the complex plane. Then what is the absolute value of its complex conjugate
Since it follows that Then
The complex number has the same absolute value as a different complex number If and are both positive integers, what are and
The absolute value of is Since also has an absolute value of it follows that implying Since and are both positive integers and by assumption, the only way that holds is that and