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)#