# \ #
# "This can be done quickly by de Moivre's Theorem --" #
# \qquad \qquad \qquad "and the result comes out beautifully." #
# "Here we go:" #
# "First, let's recall de Moivre's Theorem:" #
# \qquad \qquad \qquad ( cos( \theta ) \ + \ isin( \theta ) )^n \ = \ cos( n \theta ) \ + \ isin( n \theta ). #
# "Thus:" #
# \qquad \qquad [ 5 ( cos(30^0) \ + \ isin(30^0) ) ]^3 \ = #
# "Rules of Exponents:" #
# \qquad \qquad \qquad \qquad \qquad \quad = \ 5^3 ( cos(30^0) \ + \ isin(30^0) )^3 #
# "Applying de Moivre's Theorem:" #
# \qquad \qquad \qquad \qquad \qquad \quad = \ 5^3 ( cos( 3 \cdot 30^0 ) \ + \ isin( 3 \cdot 30^0) ) #
# \qquad \qquad \qquad \qquad \qquad \quad = \ 5^3 ( cos( 90^0 ) \ + \ isin( 90^0) ) #
# \qquad \qquad \qquad \qquad \qquad \quad = \ 5^3 ( 0 \ + \ ( i \cdot 1) ) #
# \qquad \qquad \qquad \qquad \qquad \quad = \ 5^3 ( i ) #
# \qquad \qquad \qquad \qquad \qquad \quad = \ 125 ( i ) #
# \qquad \qquad \qquad \qquad \qquad \quad = \ 125i. #
# \ #
# "Thus:" #
# \qquad \qquad \qquad \qquad \quad [ 5 ( cos(30^0) \ + \ isin(30^0) ) ]^3 \ = \ 125i. #
