Mathematics: What is √-11 in the form a+bi?

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What is √-11 in the form a+bi? - id119737957, takaralocklear

krystenlitten

13.02.2022

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 $0+\sqrt{11}i$ .

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