2.1.1 So­lu­tion math­c­plx-a

Ques­tion:

Mul­ti­ply out $(2+3{\rm i})^2$ and then find its real and imag­i­nary part.

An­swer:

Mul­ti­ply­ing out the square gives $2^2+12{\rm i}+(3{\rm i})^2$. Since ${\rm i}^2$ $\vphantom0\raisebox{1.5pt}{$=$}$ $\vphantom{0}\raisebox{1.5pt}{$-$}$1, you get $-5+12{\rm i}$. This means that the real part is $\vphantom{0}\raisebox{1.5pt}{$-$}$5 and the imag­i­nary part 12.