## mathslover 2 years ago Convert into polar form : (-1/2) + i ( $$\frac{-\sqrt{3}}{2}$$ )

1. mathslover

(-1/2) + i ( $$-\frac{\sqrt{3}}{2}$$ )

2. mathslover

I got : cos ( 4 pi/3 ) + sin ( 4 pi/3)

3. mathslover

But the book says : cos ( - 2pi/3 ) + i sin ( - 2pi/3). Which is also right...

4. Azteck

isin

5. Azteck

You're wrong.

6. mathslover

Sorry typing mistake I meant i sin 4pi/3

7. mathslover

^ cos ( 4 pi/3 ) + i sin(4pi/3)

8. Azteck

Find the absolute value of this: $\left| -\frac{ 1 }{ 2 } -\frac{ i \sqrt{3} }{ 2 }\right|$

9. mathslover

So which should I prefer more ? -2pi/3 or 4 pi/3

10. Azteck

So $=\sqrt{(-\frac{ 1 }{ 2 })^2+(-\frac{ \sqrt{3} }{ 2 })^2}$

11. Azteck

So r=1

12. Azteck

Now draw it.

13. Azteck

Drawing it gives you a way better picture of what the angle is.

14. mathslover

$\large{\sqrt{ (\frac{-1}{2} )^2 + ( \frac {- \sqrt{3}}{2})^2}}$ right so it is : $$\1$$

15. Azteck

|dw:1359153193735:dw|

16. Azteck

You took the other angle

17. Azteck

You go backwards meaning it will be negative.

18. mathslover

By the diagram I think that the angle theta will surely lie in the III quadrant i.e. 4 pi /3

19. mathslover

Ok got it thanks.

20. Azteck

If it's in the third of fourth quadrant go backwards.

21. Azteck

third or fourth*