Respuesta :

frika

Answer:

[tex]3\sqrt{2}[/tex]

Step-by-step explanation:

For the complex number [tex]a+bi,[/tex] the absolute value is [tex]\sqrt{a^2+b^2}[/tex]

Given the complex number [tex]-4-\sqrt{2}i.[/tex] For this complex number,

[tex]a=-4\\ \\b=-\sqrt{2},[/tex]

then the absolute value is

[tex]\sqrt{(-4)^2+(-\sqrt{2})^2}=\sqrt{16+2}=\sqrt{18}=3\sqrt{2}[/tex]

adioabiola

Here, we are required to find the absolute value of: -4 - √2i.

The expression -4 - √2i can be rewritten as;

-4 + (-√2)i.

Generally, complex numbers take the form;

  • a + i√b

  • a + i√band the absolute value is given as;

  • a + i√band the absolute value is given as;√(a² + b²)

Therefore, the absolute value of -4 + (-√2)i is;

√(-4)² + (-√2)² = √16+2

= √18 = √(9 × 2)

= 3√2

Therefore, the absolute value of -4 - √2i is 3√2.

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