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 [tex]12-\sqrt{(8}[/tex]
where [tex]\sqrt{8}[/tex] can be written as
[tex]\sqrt {4 \cdot 2 \cdot -1}[/tex]
Now using the below radical rule which states that
[tex]\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}[/tex]
Then,
[tex]\sqrt {4 \cdot 2 \cdot (-1)}[/tex]
=> [tex]\sqrt {4} \cdot \sqrt {2} \cdot \sqrt { -1}[/tex]
=> [tex]2 \cdot \sqrt {2} \cdot \sqrt {-1}[/tex]-----------------(1)
Also we know that
[tex]\sqrt {-1}= i[/tex]---------------------(2)
substituting (2) in (1)
we get
=> [tex]2 \cdot \sqrt {2} \cdot i[/tex]
=> [tex]2i \cdot \sqrt {2}[/tex]
=> [tex]2i \cdot 1.414[/tex]
=> 2.828i
