Answer:
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
[tex]r=\sqrt{a^{2}+b^{2}}[/tex]
Ф = [tex]tan^{-1}\frac{b}{a}[/tex]
* 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
