Question

What is the trigonometric form of `(-3+12i)`?

Answer 1

`sqrt153[cos(1.81) + isin(1.81)]`

Explanation:

To convert to trig. form , require r , the modulus and `theta,`
the argument.

`• r =sqrt(x^2 + y^2)`

`• theta = tan^-1 (y/x)`

Here x = -3 and y = 12

`rArr r = sqrt((-3)^2 + 12^2) = sqrt(9+144) = sqrt153`

[ -3 + 12i is a point in the 2nd quadrant and care must be taken to ensure that `theta color(black)(" is in this quadrant")`]

`theta = tan^-1(12/-3) = tan^-1(-4) = -1.33color(black)(" radians")`

and so `theta = (pi-1.33) = 1.81color(black)(" radians")`

`rArr (-3+12i) = sqrt153[cos(1.81) + isin(1.81)]`