Question 235867
Use the Argand plane where multiplication
is done by multiplying amplitudes and adding
angles of the rotating vectors
{{{sqrt(3)/2 + i/2}}} = {{{sqrt((sqrt(3)/2)^2 + (1/2)^2)}}} angle 30 degrees
{{{sqrt((sqrt(3)/2)^2 + (1/2)^2)}}} angle 30 degrees = {{{1}}} angle 30 degrees
{{{i = (sqrt(3)/2 + i/2)^3}}}
{{{i}}} = {{{1}}} angle 90 degrees
{{{1}}} angle 90 degrees  = {{{1^3}}} angle {{{30 + 30 + 30}}}degrees
{{{1}}} angle 90 degrees = {{{1}}} angle 90 degrees
It is best to draw this. The advantage is that the exponent could
be any size and you just add angles and raise 1 number to a power