Question

Write z = 2(cos(5pi/6) + i sin(5pi/6)) in rectangular form.

Answer 1

answer is ( root 3 +i )

Answer 2

z = (-√3 + i)

Explanation:

We have to write
`z=2[cos((5\pi )/(6))+isin((5\pi )/(6))]` in the rectangular form.

We will simplify this equation

`z=2[cos((5\pi )/(6))+isin((5\pi )/(6))]`

Since
`cos((5\pi )/(6))=-(√(3) )/(2)`

and
`sin((5\pi )/(6))=(1)/(2)`

Now we put the values in the equation

`z=2[-(√(3) )/(2) +i((1)/(2)) ]`

z = (-√3 + i)

Therefore the answer is z = -√3 + i