Question

What is the irrational conjugate of `1+sqrt8`? complex conjugate of `1 + sqrt(-8)`?

Answer 1

`1-sqrt 8 and 1-sqrt(-8)=1-i sqrt 8`, where i symbolizes `sqrt(-1)`.

Explanation:

The conjugate of the irrational number in the form

`a+bsqrt c`,

where c is positive and a, b and c are rational (including computer

string-approximations to irrational and transcendental numbers) is

a-bsqrt c#'

When c is negative, the number is termed complex and the

conjugate is

`a+ibsqrt(|c|)`, where`i = sqrt(-1)`.

Here, the answer is

`1-sqrt 8 and 1-sqrt(-8)=1-i sqrt 8`, where i symbolizes `sqrt(-1)`