a+bi in trig form is r(cos\theta+isin\theta), where:
- r=sqrt(a^2+b^2)
- \theta=abs(arctan(b/a))
(5+3i)(3+2i)~=(r_1(cos\theta_1+isin\theta_1))(r_2(cos\theta_2+isin\theta_2))
=r_1r_2(cos(\theta_1+\theta_2)+isin(\theta_1+\theta_2))
=sqrt(5^2+3^2)sqrt(3^2+2^2)(cos(abs(arctan(3/5))+abs(arctan(2/3)))+isin(abs(arctan(3/5))+abs(arctan(2/3))))
~~sqrt(34)sqrt(13)(cos(64.65)+isin(64.65))
=sqrt(442)(cos(64.65)+isin(64.65))
~~21.02(cos(64.65)+isin(64.65))
Given tantheta_1=3/5 and tantheta_1=2/3
tantheta=(3/5+2/3)/(1-3/5xx2/3)=(19/15)/(3/5)=19/9
and in exact form we can write product as
sqrt442(cos(arctan(19/9))+isin((arctan(19/9)))
