can someone please give the definition for i= √-1?

Question

aka i²=-1.

i know i is an imaginary number, and if the number inside the square root is negative then the result is an imaginary number.

Answer 1

√(ab) = (√a)(√b)

√(-b) = (√-1)(√b)

√(-b) = i (√b)

Answer 2

A little bit of insight is that the roots of any polynomial function with real coefficients , that is roots of

f(x) = 0 where f is polynomial of any degree with real coefficients are in the from:

a + b i ( in other words a general complex number) with a and b being real numbers.

This is important because it means that while i is involved, that is the end of it. Nothing more complicated is needed.

for example sqrt( i ) = ..707 + .707 i

.707 is actually sqrt(2) /2