Question 178489

{{{(1/2 + i)^2}}} Start with the given expression.



{{{(1/2 + i)*(1/2 + i)}}} Expand.



{{{(1/2)(1/2)+(1/2)(i)+(i)(1/2)+(i)(i)}}} FOIL.



{{{1/4+(1/2)i+(1/2)i+i^2}}} Multiply.



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



{{{1/4+(1/2)i+(1/2)i-1}}} Multiply.



{{{-3/4+i}}} Combine like terms.



So {{{(1/2 + i)^2=-3/4+i}}}.