Write the complex number 12 16i in trigonometric form rcos

Write the complex number -12 + 16i in trigonometric form r(cos theta + i sin theta), with theta in the interval (0 degree, 360 degree)

the trignometric form of z = a + bi is z = r ( cos(theta) + i sin (theta) )

where r = |a + bi| is the modulus of z, and tan = b / a . is called the argument of z.

Normally, we will require 0 < 2.

given z = -12 + 16 i

then r= sqrt ( ( -12 )^2 + 16^2 )

=sqrt ( 144 + 256 )

r ==> 20

tan( theta ) = 16 / -12

tan ( theta ) = -4 / 3

theta = tan^-1( -4 / 3 )

theta = -53.1301023542

then

z = 20 ( cos(-53.1301023542) + i sin (-53.1301023542))

z = 20 ( 0.6 + i -0.8 )