Write the complex number 9 12i in trigonometric form rcos t

Write the complex number -9 + 12i in trigonometric form r(cos theta + i sin theta), with theta in the interval [0 degree, 360 degree]

Solution

Solution:

trigonometric form is as follows:

r(cos() + isin())

r = sqrt(real^2 + imaginary^2)
r = sqrt((-9)^2 + (12)^2)
r = sqrt(81 + 144)
r = sqrt(225)
r = 15

= tan^-1(imaginary/real)
= tan^-1(12/(-9))
= tan^-1(-4/3)
= 306.87 degree

so trig form:

15(cos(306.87) + isin(306.87))