Question

What is the absolute value of the complex number -4-sqrt2i

Answer 1

=√18

Explanation:

The absolute value of a complex number is its distance from zero on graph. The formula for absolute value of a complex number is:

|a+bi|= √(a^2+b^2 )

where a is the real part of the complex number and b is the imaginary part of the complex number.

So for the given number,

a= -4

b=-√2

Putting in the formula:

|-4-√2 i|= √((-4)^2+(-√2)^2 )

= √(16+2)

=√18 ..

Answer 2

`3 √(2) \: units`

EXPLANATION

The absolute value of the complex number

`|a +b i| = \sqrt{ {a}^(2) + {b}^(2) }`

This is also known as the modulus of the complex number.

This implies that:

`| - 4 - √(2) i| = \sqrt{ {( - 4)}^(2) + {( - √(2) )}^(2) }`

`| - 4 - √(2) i| = √( 16 +2 )`

We simplify further to get;

`| - 4 - √(2) i| = √( 18 ) = 3 √(2) \: units`