Simplify $(7-2i)(7+2i)$. Found difference between mine and solution guide's and didn't know why. I looked up the solution guide and found out:
$(7-2i)(7+2i)$
$=49-(2i)^2$
$=49+4$
$=53$
Why the unknown "$i$" just disappeared$?$ I supposed it might be:
$(7-2i)(7+2i)$
$=49-(2i)^2$
$=49-4i$
does it?
May someone tell me which one is right and tell me the reasons? Thank you so much.

What you did wrong is that $(2i)^2$ is not $4i$, but rather $4i^2$, which is equivalent to $-4$.
