The imaginary number $i$ is defined such that $i^2=-1$. What is the value of $(1 - i \sqrt {5}) ( 1 + i\sqrt {5})$?

Imaginary number is $i=\sqrt {-1}$

Value of $(1-i\sqrt{5})(1+i\sqrt{5})$

It is in the form of $(a+b)(a-b)=a^2-b^2$

So,

$(1-i\sqrt{5})(1+i\sqrt{5})={(1)}^2-{(i\sqrt {5})}^2$

$\Rightarrow 1-(i^2\times 5)$

$\Rightarrow 1-(-1\times 5)$

$\Rightarrow 6$

$(1-i\sqrt{5})(1+i\sqrt{5})=6$