Convert the complex number 2 - 2 (sqrt 3) i into its polar representation.

4 <-60

A complex number in rectangular form is Z, where Z = a + bi.
In the given above 2-2(sqrt 3)i. In order to change it into polar form ( z= r (cos theta + i sin theta) ) or r < theta, we have to find r first.

r = |z| =  sqrt ( a^2 + b^2)
          = sqrt (2^2 + (-2 sqrt 3)^2)
          = 4
then theta = arctan(b/a)
                 = arctan ((-2sqrt3)/2)
                 = -60 degrees
Polar form = 4 ( cos (-60) + i sin (-60))
                  = 4 < -60 degrees

answer:

b. 1/3(7)(12)(10) –1/3 π(32)(10)

d. 280 – 30π

step-by-step explanation: