Determine the trigonometric form of z=-2i.

z = -2i. To find the trigonometric
form

We know that if z = x+yi is the Cartesian form, then 
r*cost + i*sint is the trigonometric form  of x+yi. Here r = (x^2+y^2)^(1/2) ,  rcost =
x, r*sin t = y and t = arc tan (y/x).

Therefore z =
0+(-2*i)

r = {0^2+(-2)^2}^(/2) =
2.

x = 0 = 2cost and y= -2i = 2i*sint. So t =  arc tan
(-2/0) = -pi/2.

So -2i = 2cos(-pi)/2+ i*sin
(-pi/2).

So 2cos(-pi)/2+ i*sin
(-pi/2) is the trigonometric form of -2i.