Question

Express the complex number in trigonometric form.

-2 + 2 sqrt(3) i

Answer 1

Hello,

-2+i*2√3=4(cos 120°+i sin 120°)

Answer 2

Explanation:

Okay...

a+ib=r (costheta+isintheta)

r=sqrt a^2+b^2

r=sqrt (-2)^2+2 sqrt 3^2

r=4

theta= tan^-1 (y/x) or (b/a)

theta= tan^-1 (2 sqrt 3/-2)

theta=tan^-1(-sqrt 3)

theta=-60

180-60=120

(we know that theta is in the 2nd quadrant because ALL Students Take Calculus. All values are positive in quadrant one, Sin is positive in quadrant two, Tangent is positive in Quadrant three, and Cosine is positive in quadrant four. Since our y-value (sin) is positive it must occur in the 2nd quadrant. That is why I subtracted it from 180.

Convert degrees to radians: 120 times pi/180 =2pi/3

theta=2pi/3

So now we have our r value (4) and theta value (2pi/3). All we need to do now is substitute.

a+ib= 4(cos 2pi/3+isin2pi/3)