HOW TO FIND ABSOLUTE VALUE OF COMPLEX NUMBER

Find the absolute value of the complex numbers given below :

Problem 1 :

4 + 3i

Solution :

Comparing the given complex number with the general form of a complex number a + ib, we get

a = 4 and b = 3

= √(4² + 3²)

= √(16 + 9)

= √25

= 5

So, the absolute value of the given complex number is 5.

Problem 2 :

-√15 + i √15

Solution :

Comparing the given complex number with the general form of a complex number a + ib, we get

a = -√15 and b = √15

= √(-√15)² + (√15)²

= √15 + 15

= √30

So, the absolute value of the complex number is √30.

Problem 3 :

Solution :

Since the given is in the form of polar form, we have to convert it into rectangular form and then find the absolute value.

Finding absolute value :

a = 0 and b = -1

= 3√0² + (-1)²

= 3√1

= 3

So, the absolute value of the given complex number is 3.

Problem 4 :

Solution :

Finding absolute value :

a = 0 and b = 1

= √21 (√0² + 1²)

= √21 (1)

= √21

So, the absolute value of the given complex number is √21.

Problem 5 :

(-2√3 - 2i)

Solution :

Let z = (-2√3 - 2i)

Comparing the given complex number with the general form of a complex number a + ib, we get

a = -2√3 and b = -2

= √(-2√3)² + (-2)²

Distributing square separately, we get

= √(4(3) + 4)

= √(12 + 4)

= √16

= 4

So, the absolute value of the complex number is 4.

Problem 6 :

Solution :