Question 173284
{{{(5-2i)^2}}} Start with the given expression.



{{{(5-2i)*(5-2i)}}} Expand



{{{(5)(5)+(5)(-2i)+(-2i)(5)+(-2i)(-2i)}}} FOIL.



{{{25-10i-10i+4i^2}}} Multiply.



{{{25-10i-10i+4(-1)}}} Replace {{{i^2}}} with {{{-1}}}. Note: {{{i^2=-1}}}.



{{{25-10i-10i-4}}} Multiply.



{{{21-20i}}} Combine like terms.



So {{{(5-2i)^2=21-20i}}}.



So the expression is now in standard form {{{a+bi}}} where {{{a=21}}} and {{{b=-20}}}