Convert to Trigonometric forms first
-3+6i=3sqrt5[cos(tan^-1((6)/(-3)))+i sin(tan^-1((6)/(-3)))]−3+6i=3√5[cos(tan−1(6−3))+isin(tan−1(6−3))]
-4+7i=sqrt65[cos(tan^-1((7)/(-4)))+i sin(tan^-1((7)/(-4)))]−4+7i=√65[cos(tan−1(7−4))+isin(tan−1(7−4))]
Divide equals by equals
(-3+6i)/(-4+7i)=−3+6i−4+7i=
(sqrt45/sqrt65)[cos(tan^-1((6)/(-3))-tan^-1((7)/(-4)))+i sin(tan^-1((6)/(-3))-tan^-1((7)/(-4)))](√45√65)[cos(tan−1(6−3)−tan−1(7−4))+isin(tan−1(6−3)−tan−1(7−4))]
Take note of the formula:
tan (A-B)=(Tan A-Tan B)/(1+Tan A* Tan B)tan(A−B)=tanA−tanB1+tanA⋅tanB
also
A-B=Tan^-1 ((Tan A-Tan B)/(1+Tan A* Tan B))A−B=tan−1(tanA−tanB1+tanA⋅tanB)
(3sqrt(13))/13[cos(tan^-1((-1)/18))+i*sin(tan^-1((-1)/18))]3√1313[cos(tan−1(−118))+i⋅sin(tan−1(−118))]
(3sqrt(13))/13[cos(6.2276868019339)+i*sin(6.2276868019339)]" "3√1313[cos(6.2276868019339)+i⋅sin(6.2276868019339)] radian angles
(3sqrt(13))/13[cos(356.82016988014^@)+i*sin(356.82016988014^@)]" "3√1313[cos(356.82016988014∘)+i⋅sin(356.82016988014∘)]
