Question 202871
I'm assuming that the expression is {{{(-2+sqrt(-4))^2}}} right????



{{{(-2+sqrt(-4))^2}}} Start with the given expression.



{{{(-2+sqrt(-1*4))^2}}} Factor



{{{(-2+sqrt(-1)*sqrt(4))^2}}} Break up the square root.



{{{(-2+i*2)^2}}} Replace {{{sqrt(-1)}}} with "i". Take the square root of 4 to get 2.



{{{(-2+2i)^2}}} Rearrange the terms.



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



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



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



{{{4-4i-4i-4}}} Multiply.



{{{-8i}}} Combine like terms.



So {{{(-2+sqrt(-4))^2=-8i}}}.