How do you express the complex number in trigonometric form: -2i?

1 Answer
Jun 13, 2016

Answer:

Reqd. form #= 2(cos3pi/2+sin3pi/2).#

Explanation:

The complex no. #z=x+iy# can be expressed in trigo. form #rcistheta=r(costheta+isintheta)# by using the conversion formula #x=rcostheta, y=rsintheta, r=sqrt(x^2+y^2).#
Here, we have, #x=0, y=-2.#
Clearly, #r=2.#
Next pair of eqns. is #0=2costheta, -2=2sintheta.#
#:. costheta=0, sintheta=-1.# #theta=3pi/2#
#:.#Reqd. form #= 2(cos3pi/2+sin3pi/2).#