Question

Rewrite the rectangular form of the complex number z= - sq root 3+i in its equivalent polar form. Approximate all angle measures to the nearest degree.

z=10(cos(-30)+ i sin(-30))
z=2(cos 150+ i sin 150)
z=2(cos(-30)+ i sin(-30))
z=10 (cos 150+ i sin 150)

Answer 1

z=2(cos 150+ i sin 150) is the correct answer. I just did this lesson and got it right, hope this helps!

Answer 2

Given a complex number :
`z = a + bi`


`r = √(a^2 + b^2) \\ \\ r = \sqrt{(-√(3))^2+1^2} \\ \\ r = 2`

To determine the angle:

`\theta = tan^(-1) ((b)/(a)) \\ \\ \theta = tan^(-1) (-(1)/(√(3))) \\ \\ \theta = -30, 150`
The 'cos' term is negative and the 'sin' term is positive, therefore theta must be in 2nd quadrant.

`\theta = 150`

Final Answer:

`z = 2(cos 150 + i sin 150)`