Question

How do you divide `( -4i+2) / (i+7)` in trigonometric form?

Answer 1

In trigonometric form : `0.632[cos(-71.565)+i sin(-71.565)]`

Explanation:

`(-4i+2)/(i+7) = ((-4i+2)(i-7))/((i+7)(i-7)) = (-4*i^2-14+30*i)/(i^2-7^2) =(-1/50)*(-10+30i)=0.2-0.6i`. Let `Z=0.2-0.6i` Modulas Z= `sqrt(0.2^2+(-0.6)^2) = .632` Argument Z `theta=tan^-1((-0.6)/(0.2))=tan^-1(-3)=-71.565^0` Hence Z expressed in trigonometric form: `0.632[cos(-71.565)+i sin(-71.565)]`[Ans]