# ABSOLUTE VALUE OF A COMPLEX NUMBER

Absolute value of a complex number :

The absolute value of a complex number , a + ib (also called the modulus ) is defined as the distance between the origin (0,0) and the point (a,b) in the complex plane.

To find the absolute value of a complex number, we have to take square root of the sum of squares of real and part imaginary part respectively.

|a + ib| = √(a² + b²) ## Absolute value of a complex number - Examples

Let us see some example problems based on the concept.

Example 1 :

Find the absolute value of 7 - i

Solution :

|7 - i| = √(7² + (-1)²)

=  √(49 + 1

=  √50

=  √5 x 5 x 2

=  5 √2

Example 2 :

Find the absolute value of -5 - 5i

Solution :

|-5 - 5i| = √[(-5)² + (-5)²]

=  √25 + 25

=  √50

=  √5 x 5 x 2

=  5 √2

Example 3 :

Find the absolute value of 3 - 6i

Solution :

|3 - 6i| = √3² + (-6)²

=  √9 + 36

=  √45

=  √3 x 3 x 5

=  3 √5

Example 4 :

Find the absolute value of 10 - 2i

Solution :

|10 -2i| = √10² + (-2)²

=  √100 + 4

=  √104

Example 5 :

Find the absolute value of -4 - 8i

Solution :

|-4 - 8i| = √(-4)² + (-8)²

=  √16 + 64

=  √80

=  √2 x 2 x 2 x 2 x 5 = 4 √5

Example 6 :

Find the absolute value of -4 + 10i

Solution :

|-4 + 10i| = √(-4)² + 10²

=  √16 + 100

=  √116

=  √2 x 2 x 29 = 2 √29

Example 7 :

Find the absolute value of 1 - 8i

Solution :

|1 - 8i| = √1² + (-8)²

=  √1 + 64

=  √65

Example 8 :

Find the absolute value of -4 - 3i

Solution :

|-4 - 3i| = √(-4)² + (-3)²

=  √16 + 9

=  √25 ==> √5 x 5 ==> 5

Example 9 :

Find the absolute value of -1 + 5i

Solution :

|-1 + 5i| = √(-1)² + 5²

=  √1 + 25

=  √26

Example 10 :

Find the absolute value of 8 - 3i

Solution :

|8 - 3i| = √8² + (-3)²

=  √64 + 9

=  √73

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