Question

How do you multiply `(-2-5i)(-1-6i)` in trigonometric form?

Answer 1

In trigonometric form : `Z=32.46*(cos 148.74+ i sin 148.74)`

Explanation:

`(-2-5i)(-1-6i)= 2+17i+30i^2=2-30+17i= -28+17i` since `i^2=-1`
Modulas `r= sqrt ((-28)^2+17^2) =sqrt 1073 =32.46`
Argument `theta =180- tan^-1(17/28)= 148.74^0` As it lies on the 2nd quadrant the angle has been subtracted from `180^0` In trigonometric form : `Z=32.46*(cos 148.74+ i sin 148.74)`[Ans]