Question 207549
{{{(2+3i)*(2+3i)}}} Start with the given expression.



{{{(2+3i)^2}}} Expand



{{{(2)(2)+(2)(3i)+(3i)(2)+(3i)(3i)}}} FOIL.



{{{4+6i+6i+9i^2}}} Multiply.



{{{4+6i+6i+9(-1)}}} Replace {{{i^2}}} with {{{-1}}}. Note: {{{i^2=-1}}}.



{{{4+6i+6i-9}}} Multiply.



{{{-5+12i}}} Combine like terms.



So {{{(2+3i)^2=-5+12i}}}.



So the expression is now in standard form {{{a+bi}}} where {{{a=-5}}} and {{{b=12}}}