In trigonometric form, a complex number looks like this:
#a + bi = c*cis(theta)#
where #a#, #b# and #c# are scalars.
Let two complex numbers:
#-> k_(1) = c_(1)*cis(alpha)#
#-> k_(2) = c_(2)*cis(beta)#
#k_(1)*k_(2) = c_(1) * c_(2) * cis(alpha) * cis(beta) =#
#= c_(1) * c_(2) * (cos(alpha) + i*sin(alpha)) * (cos(beta) + i*sin(beta))#
This product will end up leading to the expression
#k_(1)*k_(2) =#
#= c_(1)*c_(2)*(cos(alpha + beta) + i*sin(alpha + beta)) =#
#= c_(1)*c_(2)*cis(alpha+beta)#
By analyzing the steps above, we can infer that, for having used generic terms #c_(1)#, #c_(2)#, #alpha# and #beta#, the formula of the product of two complex numbers in trigonometric form is:
#(c_(1) * cis(alpha)) * (c_(2) * cis(beta)) = c_(1)*c_(2)*cis(alpha+beta)#
Hope it helps.
