Question

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

Answer 1

Answer: c

Explanation:

edge

Answer 2

C.
`z = -20√(3)-i\,20`

Explanation:

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

`z = a+i\,b` (1)

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

`a = r\cdot \cos \theta` (2)

`b = r\cdot \sin \theta` (3)

Where:

`r` - Magnitude of the complex number, dimensionless.

`\theta` - Direction of the complex number, measured in radians.

If we know that
`r = 40` and
`\theta = (7\pi)/(6)`, then the rectangular form of the number is:

`a = 40\cdot \cos (7\pi)/(6)`

`a = -20√(3)`

`b = 40\cdot \sin (7\pi)/(6)`

`b = -20`

The rectangular form of
`z=40\cdot\left(\cos (7\pi)/(6)+i\,\sin (7\pi)/(6)\right)` is
`z = -20√(3)-i\,20`. The correct answer is C.