Question

How do you solve `(x-2)^2=-3`?

Answer 1

`(1)` : In `RR`, the soln. set is `phi`.

`(2)` : `In CC`, the soln set is `{2+-isqrt3 }.`

Explanation:

In `RR`, the soln. set is `phi`; as, in `RR, (x-3)^2>=0`

In `CC` since, `i=sqrt(-1)`, we have, `(x-2)^2=-3=(isqrt3)^2`

`rArr x-2=+-isqrt3 rArr x=2+-isqrt3`