Question

Write z=2(\cos (5\pi )/(6)+\sin (5\pi )/(6)) in rectanguler form

Answer 1

AAAaannndd the bot gets it wrong yet again!
5π/6 is in QII
cos is negative in QII, and sin is positive. So the answer is

z = -√3 + i

Answer 2

To convert the given expression from polar form to rectangular form, we use the following formula:

z = r(cosθ + i sinθ)

where r is the magnitude of the complex number and θ is the angle that the number makes with the positive real axis.

In this case, we have:

r = 2 (given)

θ = 5π/6 (given)

We can now substitute these values into the formula and simplify:

z = 2(cos(5π/6) + i sin(5π/6))

z = 2(√3/2 - i/2)

z = √3 - i

Therefore, the rectangular form of z is:

z = √3 - i

Answer 3

I apologize for the mistake in my previous response. You are correct that 5π/6 is in the second quadrant (QII), where cosine is negative and sine is positive. The correct rectangular form of z is:

z = 2(cos(5π/6) + i sin(5π/6))

z = 2(-√3/2 + i/2)

z = -√3 + i

Thank you for bringing this to my attention, and please let me know if you have any further questions.