absolute value (complex number)

Absolute Value (Complex Number)

What is absolute value (complex number) in math?

In mathematics, the absolute value of a complex number is a measure of its distance from the origin in the complex plane. It is also known as the modulus or magnitude of the complex number. The absolute value of a complex number is always a non-negative real number.

What knowledge points does absolute value (complex number) contain?

To understand the concept of absolute value of a complex number, one should have knowledge of complex numbers, the complex plane, and the distance formula.

What is the formula for absolute value (complex number)?

The formula to calculate the absolute value of a complex number z = a + bi, where a and b are real numbers, is given by:

|z| = √(a^2 + b^2)

How to apply the absolute value (complex number) formula?

To apply the formula, substitute the real and imaginary parts of the complex number into the formula and perform the necessary calculations. The result will be the absolute value of the complex number.

What is the symbol for absolute value (complex number)?

The symbol used to represent the absolute value of a complex number is two vertical bars surrounding the complex number. For example, |z| represents the absolute value of the complex number z.

What are the methods for absolute value (complex number)?

There are a few methods to find the absolute value of a complex number:

1. Using the formula: Substitute the real and imaginary parts into the formula and calculate the square root of the sum of their squares.
2. Geometrically: Plot the complex number on the complex plane and measure its distance from the origin.
3. Using the properties of complex numbers: If the complex number is in the form a + bi, the absolute value can be found using the Pythagorean theorem.

Solved Example on absolute value (complex number):

Example 1: Find the absolute value of the complex number z = 3 + 4i.

Solution: Using the formula, we substitute a = 3 and b = 4 into the formula:

|z| = √(3^2 + 4^2) = √(9 + 16) = √25 = 5

Therefore, the absolute value of the complex number z = 3 + 4i is 5.

Practice Problems on absolute value (complex number):

1. Find the absolute value of the complex number z = -2 + 3i.
2. Calculate the absolute value of the complex number z = 5 - 12i.
3. Determine the absolute value of the complex number z = -1 - i.

FAQ on absolute value (complex number):

Q: Can the absolute value of a complex number be negative? A: No, the absolute value of a complex number is always a non-negative real number.

Q: What is the geometric interpretation of the absolute value of a complex number? A: Geometrically, the absolute value of a complex number represents its distance from the origin in the complex plane.

Q: How is the absolute value of a complex number related to its conjugate? A: The absolute value of a complex number is equal to the square root of the product of the complex number and its conjugate.