#z = sin(105^circ) + icos(75^circ) #
#=> z = ( sqrt(6) + sqrt(2)) / 4 + i ( (sqrt(6) - sqrt(2) ) / 4 )#
Polar form is: #z = (r,theta) = re^(itheta) #
#r# is simply the modulus of the complex number, or the length from the origin #(0,0) #
#r =sqrt((( sqrt(6) + sqrt(2) )/4 )^2 + ( (sqrt(6)-sqrt(2))/4)^2 #
#=> r= 1 #
Now to find #theta #:
if #z = a+bi => theta = arctan(b/a) #
#=> theta = arctan( ((sqrt(6)-sqrt(2) )/4) / ( (sqrt(6)+sqrt(2))/4 ) ) #
#=> theta = 15^circ #
Hence the polar coordinate is:
#z = (1,15^circ) = e^(15^circ i ) #