12. write 18(cos169° + isin169°) in rectangular form. round numerical entries in the answer to two decimal places.

The rectangular form is z = -17.67 + i 3.43

Step-by-step explanation:

* Lets explain how change the modulus form to the rectangular form

- The rectangular form of a complex number is given by

  z = a + bi , where

  a = r cos Ф and b = r sin Ф

- The modulus form of the complex number is

  z = r(cos Ф + i sin Ф) where

  Ф =

* Lets solve the problem

∵ z = 18(cos(169)° + i sin(169)°)

∵ z = r(cos Ф + i sin Ф)

∴ r = 18 and Ф = 169°

∵ z = a + ib , where

   a = r cos Ф and b = r sin Ф

∴ a = 18 cos(169)°

∴ b = 18 sin(169)°

- Angle Ф lies in the 2nd quadrant (90° < Ф < 180°)

∵ sin(169)° is positive ⇒ (sine in the 2nd quadrant positive)

∵ cos(169)° is negative ⇒ (cosine in the 2nd quadrant is negative)

∴ a = -17.67

∴ b = 3.43

∴ z = -17.67 + i 3.43

* The rectangular form is z = -17.67 + i 3.43

ou would have 12 of each

step-by-step explanation:

ok one would be money, and the other would be refreshments or something similar. if each bag of popcorn is 5.00 and each drink is half of that that means drinks are 2.50 the proper way to do that would to look and see how much of each you can buy without exceeding a limit of 30.00