Question

What is the absolute value of the complex number 4-V3/?
O 32
O 14
O 18

Answer 1

Answer:

$3\sqrt{2}$

Step-by-step explanation:

The Magnitude of a Complex Number

A complex number is expressed in rectangular form as:

$Z=a+ b\mathbf{ i}$

The absolute value or magnitude of Z is calculated as follows:

$\mid Z\mid=\sqrt{a^2+b^2}$

We are given the number

$Z=-4-\sqrt{2}\mathbf{ i}$

Here: a= -4, b=$-\sqrt{2}$

Calculating the absolute value:

$\mid Z\mid=\sqrt{(-4)^2+(-\sqrt{2})^2}$

Operating:

$\mid Z\mid=\sqrt{16+2}=\sqrt{18}$

Factoring 18:

$\mid Z\mid=\sqrt{3^2*2}$

Taking the square root of 3^2:

$\mid Z\mid=3\sqrt{2}$

Answer: $\mathbf{3\sqrt{2}}$