Question

compare and contrast the absolute value of a real number to that of a complex number​

Answer 1

Absolute value of real number and complex number

Step-by-step explanation:

Real Number:

Take for example real number |4|. The absolute value of this real number will be the distance from 0 on the number line.

So absolute value of |4| is 4.

Complex Number:

For a complex number, absolute value is not its distance on the number line, but instead it is measured on the complex number plane.

Formula for absolute value of complex number is:

 |a + bi| = √a² + b²

Example: Absolute value of a complex number, 3 + 4i, will be the distance from zero to that number on the complex plane.

|3 + 4i| = √3² + 4² = 5

Answer 2

Explanation:

In mathematics, a complex number z is written as,

z=a+ib, where a and b are real numbers.

The absolute value of the complex number z is given by:

|z| = |a+ib| = $\sqrt{a^{2} + b^{2} }$

Now,

Re-writing |z| as:

|z| = $\sqrt{(a-0)^{2}+(b-0)^{2} }$

Which represents the distance of the point (a,b) from the origin in the complex plane.

Hence, the absolute value represents the distance of the point (a,b) from the origin in the complex plane.

The absolute value of a real number is defined as |x| = x, ∀x ∈ R.

Hence, the absolute value of a real number is always positive and represents the distance of the number on the number line from zero.

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