Write the complex number in the form a + bi. 6(cos 330° + i sin 330°)

The complex number  6(cos 330° + i sin 330°) in the form of a+bi is:

3√3-3 i

Step-by-step explanation:

6(cos 330° + i sin 330°)

= 6(cos(360°-30°)+ i sin(360°-30°))

=6(cos30°- i sin30°)   (since, 360°-30° lies in fourth quadrant and cos is positive there and sin is negative)

=

Distributing 6, we get

=3√3-3 i

Hence, the complex number  6(cos 330° + i sin 330°) in the form of a+bi is:

3√3-3 i

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.