The given expression is:
[tex](a+ib)^2[/tex]Expand to get:
[tex]\begin{gathered} (a+ib)^2=a^2+i^2b^2+2abi \\ =a^2-b^2+2abi \end{gathered}[/tex]The value is as above since it is given that i^2=-1.
So the expansion is:
[tex](a+ib)^2=a^2-b^2+2abi[/tex]The blank should be:
[tex]a^2-b^2[/tex]