Question

What is √-11 in the form a+bi?

Answer 1

Given:

The number is $\sqrt{-11}$.

To find:

The a+bi form of given number.

Solution:

We have,

$\sqrt{-11}$

It can be written as

$\sqrt{-11}=\sqrt{-1\times 11}$

$\sqrt{-11}=\sqrt{-1}\times \sqrt{11}$      $[\because \sqrt{ab}=\sqrt{a}\sqrt{b}]$

$\sqrt{-11}=i\times \sqrt{11}$      $[\because \sqrt{-1}=i]$

$\sqrt{-11}=\sqrt{11}i$

Here, real part is missing. So, it can be taken as 0.

$\sqrt{-11}=0+\sqrt{11}i$

So, a = 0 and $b=\sqrt{11}$.

Therefore, the a+bi form of given number is $0+\sqrt{11}i$.