Answer:
The rectangular form is z = -17.67 + i 3.43
Step-by-step explanation:
* <em>Lets explain how change the modulus form to the rectangular form</em>
- The rectangular form of a complex number is given by
<em>z = a + bi</em> , where
<em>a = r cos Ф</em> and <em>b = r sin Ф</em>
- The modulus form of the complex number is
<em>z = r(cos Ф + i sin Ф)</em> where
Ф =
* <em>Lets solve the problem</em>
∵ 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
∴ <em>a = 18 cos(169)°</em>
∴ <em>b = 18 sin(169)°</em>
- 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)
∴ <em>a = -17.67</em>
∴ <em>b = 3.43</em>
∴ z = -17.67 + i 3.43
* The rectangular form is z = -17.67 + i 3.43