Any complex equation in the form of a+bia+bi i.e. (vector form) can be written as re^(thetai)reθi (rectangular form)
Here,
r rarrr→ magnitude of the vector, and
theta rarrθ→ the angle between the vector form and the components
now, re^(thetai)reθi is equivalent to r(costheta +isintheta)r(cosθ+isinθ)
this tells us,
a=rcosthetaa=rcosθ
and b=rsinthetab=rsinθ
thus, by solving the 2 above equations, r=sqrt(a^2+b^2)r=√a2+b2
and theta=tan^-1(b/a)θ=tan−1(ba)
So, solving for (-2-9i)(−2−9i),
r_1 = sqrt85r1=√85
theta_1=77.47θ1=77.47 degrees
And,solving for (-3-4i)(−3−4i),
r_2 = 5r2=5
theta_2=53.13θ2=53.13 degrees
so, we get,
(−2−9i)(−3-4i)=sqrt85 e^(77.47i)(−2−9i)(−3−4i)=√85e77.47i x 5e^(53.13i)= 5sqrt85 e^(130.6i)5e53.13i=5√85e130.6i
:. (−2−9i)(−3-4i)=5sqrt85(cos130.6+isin130.6)
:. (−2−9i)(−3-4i)=5sqrt85(-0.651+0.759i)
:. (−2−9i)(−3-4i)=(-30+35i)
