Answer:
[tex]36i^{2}+48i+16[/tex]
Step-by-step explanation:
[tex](4+6i)^{2}[/tex] is essentially [tex](4+6i)(4+6i)[/tex] (you are squaring [tex](4+6i)[/tex], so multiplying it by itself), so to simplify, you would need to distribute.
A good way to go about this is using the F.O.I.L. method, multiplying the First numbers in the parentheses, then the Outers, then Inners, and finally, Lasts.
[tex](4+6i)(4+6i)[/tex] >> [tex](4+6i)(4+6i)[/tex] >> [tex](4+6i)(4+6i)[/tex] >> [tex](4+6i)(4+6i)[/tex]
([tex](4*4)+(4*6i)+(6i*4)(6i*6i)[/tex])
After doing so, you would end up with [tex]16+24i+24i+36i^{2}[/tex], and after combining like terms, [tex]16+48i+36i^{2}[/tex].
To write the expression in standard form, though, just order the terms from highest to lowest power!
