Question 317789
{{{(1-2i)^2}}} Start with the given expression.



{{{(1-2i)(1-2i)}}} Expand



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



{{{1-2i-2i+4i^2}}} Multiply.



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



{{{1-2i-2i-4}}} Multiply.



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



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