Question 182634
{{{(3+10i)^2}}} Start with the given expression.



{{{(3+10i)*(3+10i)}}} Expand. Remember, something like {{{A^2=A*A}}}



{{{(3)(3)+(3)(10i)+(10i)(3)+(10i)(10i)}}} FOIL.



{{{9+30i+30i+100i^2}}} Multiply.



{{{9+30i+30i+100(-1)}}} Replace {{{i^2}}} with {{{-1}}}. Note: {{{i^2=-1}}}.



{{{9+30i+30i-100}}} Multiply.



{{{-91+60i}}} Combine like terms.



So {{{(3+10i)^2=-91+60i}}}.