Question #74a18

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Answer 1 · 2018-02-16T09:28:26

#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 ) #