Answer:
The trigonometric form of the complex number is 12(cos 120° + i sin 120°)
Step-by-step explanation:
* Lets revise the complex number in Cartesian form and polar form
- The complex number in the Cartesian form is a + bi
-The complex number in the polar form is r(cosФ + i sinФ)
* Lets revise how we can find one from the other
- r² = a² + b²
- tanФ = b/a
* Now lets solve the problem
∵ z = -6 + i 6√3
∴ a = -6 and b = 6√3
∵ r² = a² + b²
∴ r² = (-6)² + (6√3)² = 36 + 108 = 144
∴ r = √144 = 12
∵ tan Ф° = b/a
∴ tan Ф = 6√3/-6 = -√3
∵ The x-coordinate of the point is negative
∵ The y-coordinate of the point is positive
∴ The point lies on the 2nd quadrant
* The measure of the angle in the 2nd quadrant is 180 - α, where
α is an acute angle
∵ tan α = √3
∴ α = tan^-1 √3 = 60°
∴ Ф = 180° - 60° = 120°
∴ z = 12(cos 120° + i sin 120°)
* The trigonometric form of the complex number is
12(cos 120° + i sin 120°)
Since AB is the perpendicular bisector of IK, it separates IK into 2 equal segments. So, the two halves of IK are the same length. (From AB to K, and from AB to I) <span />
Similar triangles, so 24/32=33/32+x. cross multiply to find that 32*33=24(x+32). this gives you 1056=24x+768. subtract 768 from both sides to get 288 = 24x. divide both sides by 24 to get x=12
The answer is 69.45
hope this helps :)
Answer:
Step-by-step explanation:
