Any complex equation in the form of #a+bi# i.e. (vector form) can be written as #re^(thetai)# (rectangular form)
Here,
#r rarr# magnitude of the vector, and
#theta rarr# the angle between the vector form and the components
now, #re^(thetai)# is equivalent to #r(costheta +isintheta)#
this tells us,
#a=rcostheta#
and #b=rsintheta#
thus, by solving the 2 above equations, #r=sqrt(a^2+b^2)#
and #theta=tan^-1(b/a)#
So, solving for #(-2-9i)#,
#r_1 = sqrt85#
#theta_1=77.47# degrees
And,solving for #(-3-4i)#,
#r_2 = 5#
#theta_2=53.13# degrees
so, we get,
#(−2−9i)(−3-4i)=sqrt85 e^(77.47i)# x #5e^(53.13i)= 5sqrt85 e^(130.6i)#
#:. (−2−9i)(−3-4i)=5sqrt85(cos130.6+isin130.6)#
#:. (−2−9i)(−3-4i)=5sqrt85(-0.651+0.759i)#
#:. (−2−9i)(−3-4i)=(-30+35i)#
