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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