What is the rectangular form of z= 40(cos(7pi/6)+ i sin(7pi/6)) a. z= 20-20i rt3

b. z= 20rt3 -20 i

c. z= -20rt3 -20 i

d. z= -20-20 i rt3

C.

Step-by-step explanation:

The rectangular form of a complex number is represented by the following formula:

(1)

Where each coefficient can be determined as function of the polar components:

(2)

(3)

Where:

- Magnitude of the complex number, dimensionless.

- Direction of the complex number, measured in radians.

If we know that and , then the rectangular form of the number is:

The rectangular form of is . The correct answer is C.

(-5,-28)

i graphed to on desmos.