A SIMPLE EXPLANATION TO A CONFUSING QUERY (√𝑎b = √-𝑏√-a )
I was browsing sites and then I came across this question: This question was met with multiple replies but none of them gave satisfactory answer. Some said that this expression is only valid when at least one of the numbers a and b is positive but ideally that did not make any sense. Well I might have an explanation. It all depends on how you see the most elementary part of imaginary numbers, i.e., iota. Let us interpret iota in other way. Iota(i) is that elementary part of an imaginary number which when removed, results in a real number provided that magnitude of the number remains same. For example: √-200 = √200 √-1 Here if I remove √-1, I will get a real number. So coming to our original problem √𝑎b = √-𝑏√-a = √b√a (i)^2 Stop. Try to see that if a remove iota from the expression I will be left with √b√a (i) which still is a imaginary number. But as we defined imaginary numbers to be those numbers who become real numbers when iota is dropped, writing this step itself is wrong. H