Hang on a second, let's just summarise what we've deduced so far:

This is true because a complex number can be expressed as a+bi and b is allowed to be 0.

This is also true because $\displaystyle (bi)^2=b^2i^2=-b^2$. This ($\displaystyle -b^2$) is always negative since $\displaystyle b^2$ is always postive.

This is true since, quoting Moo, "0 is a real and imaginary number". Thanks Moo!

With regards to question 2:

The solution is n must be an even number (take a nice glance at Moo's pattern, thanks yet again).

Ps. I started writing this post after I noticed Moo and Bobak had edited some of theirs so there might not be any point in this. I guess it helps anyone else reading this thread!

Ready the sails!! weigh the anchor!

I could have been a pirate, or a financier but then I thought "why not try a more challenging career?......."