**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)

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 - 3**i**| = **√8² + (-3)²

= √64 + 9

= √73

After having gone through the stuff given above, we hope that the students would have understood "Absolute value of complex number".

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