Question

12-sqrt(-8) Complex number notation

Answer 1

Answer:

The complex number notation of  12-sqrt(-8) is 12 - 2.828i

Step-by-step explanation:

Given:

12-sqrt(-8)

To Find:

The  complex number notation of 12-sqrt(-8)

Solution:

12-sqrt(-8)  can be $12-\sqrt{(8}$

where $\sqrt{8}$ can be written as

$\sqrt {4 \cdot 2 \cdot -1}$

Now using the below radical rule which states that

$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$

Then,

$\sqrt {4 \cdot 2 \cdot (-1)}$

=> $\sqrt {4} \cdot \sqrt {2} \cdot \sqrt { -1}$

=>  $2 \cdot \sqrt {2} \cdot \sqrt {-1}$-----------------(1)

Also  we know that

$\sqrt {-1}= i$---------------------(2)

substituting  (2) in (1)

we get

=>  $2 \cdot \sqrt {2} \cdot i$

=>  $2i \cdot \sqrt {2}$

=>  $2i \cdot 1.414$

=> 2.828i