Question

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

Answer 1

Answer:

=√18

Step-by-step 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

ANSWER

$3 \sqrt{2} \: units$

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:

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

$| - 4 - \sqrt{2} i| = \sqrt{ 16 +2 }$

We simplify further to get;

$| - 4 - \sqrt{2} i| = \sqrt{ 18 } = 3 \sqrt{2} \: units$