Question

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

Answer 1

`3√(2)`

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=√(a^2+b^2)`

We are given the number

`Z=-4-√(2)\mathbf{ i}`

Here: a= -4, b=
`-√(2)`

Calculating the absolute value:

`\mid Z\mid=\sqrt{(-4)^2+(-√(2))^2}`

Operating:

`\mid Z\mid=√(16+2)=√(18)`

Factoring 18:

`\mid Z\mid=√(3^2*2)`

Taking the square root of 3^2:

`\mid Z\mid=3√(2)`

Answer:
`\mathbf{3√(2)}`