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# How to rationalise imaginary denominators ?

Last updated date: 19th Jul 2024
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Hint:An imaginary number is a number which is multiple of ‘i’. Here, ‘i’ is called iota and is equal to $\sqrt{-1}$. Check what happens to an imaginary number when we multiply it by a ‘i’ or any other imaginary number.

Let us first understand what is an imaginary number. Before that we will understand what complex number. Complex numbers is a set of those numbers that can be real or non-real numbers. We already know the real number. Every number that is present on a number line is a real number. Whereas an imaginary number is a number which is multiple of ‘i’. Here, ‘i’ is called iota and is equal to $\sqrt{-1}$. Therefore, if we have a number say ‘5i’ then, this number is an imaginary number.
We know that a rational number is a number that can be expressed in the form of a fraction of two integers where the denominator is not equal to zero. Therefore, when we say about rationalising an imaginary number, we mean to make the number a rational number.Suppose we have an imaginary number ‘xi’, where x is a real number. We know that $xi=x\times \sqrt{-1}$.
$\Rightarrow x\times \sqrt{-1}\times \sqrt{-1}\\ \Rightarrow x\times {{\left( \sqrt{(-1)} \right)}^{2}}\\ \Rightarrow x\times (-1)\\ \therefore -x$