Given:
The number is [tex]\sqrt{-11}[/tex].
To find:
The a+bi form of given number.
Solution:
We have,
[tex]\sqrt{-11}[/tex]
It can be written as
[tex]\sqrt{-11}=\sqrt{-1\times 11}[/tex]
[tex]\sqrt{-11}=\sqrt{-1}\times \sqrt{11}[/tex] [tex][\because \sqrt{ab}=\sqrt{a}\sqrt{b}][/tex]
[tex]\sqrt{-11}=i\times \sqrt{11}[/tex] [tex][\because \sqrt{-1}=i][/tex]
[tex]\sqrt{-11}=\sqrt{11}i[/tex]
Here, real part is missing. So, it can be taken as 0.
[tex]\sqrt{-11}=0+\sqrt{11}i[/tex]
So, a = 0 and [tex]b=\sqrt{11}[/tex].
Therefore, the a+bi form of given number is [tex]0+\sqrt{11}i[/tex].
