## anonymous one year ago HOW is anybody supposed to find the answer to this pre calc question???? Express the complex number in trigonometric form. -2 How am i supposed to do anything with that number? These are my choices, but I am completely lost! : 2(cos 90° + i sin 90°) 2(cos 0° + i sin 0°) 2(cos 180° + i sin 180°) 2(cos 270° + i sin 270°)

1. anonymous

z = |z|(cos Θ + i sin Θ) For yours z = -2 + 0i, so |z| = 2. The real part is the horizontal axis, so Θ = 0°

2. anonymous

you could check the answer choices, which would be one way

3. anonymous

not to disagree with @peachpi but for $$-2$$ you would have $$\theta=\pi$$ or if you are working in degrees for some unknown reason $$\theta=180^\circ$$

4. anonymous

|dw:1439175703750:dw|

5. anonymous

What is that formula called? @peachpi

6. anonymous

oh yeah. forgot about the negative

7. anonymous

it is not a formula, it is an equality between numbers $2(\cos(180)+i\sin(180))=2\times (-1+0)=-2$

8. anonymous

Ah, okay. Im getting 2(cos 0° + i sin 0°) as my answer

9. anonymous

but that cannot be correct since $$\cos(0)=1$$ not $$-1$$

10. anonymous

Im still a bit confused on the process of getting to my answer...

11. anonymous

@satellite73

12. anonymous

it is an equality between two numbers you have $$-2$$ right?

13. anonymous

the absolute value of $$-2$$ is $$2$$

14. anonymous

Right @satellite73

15. anonymous

therefore it will be $2(\cos(\theta)+i\sin(\theta))=-2$ which is only possible if $$\sin(\theta)=0$$ since $$-2$$ has no $$i$$ in it and if $$\cos(\theta)=-1$$ since $$2\times -1=-2$$

16. anonymous

so one possible value of $$\theta$$ is $$180$$ as $$\cos(180)=-1$$ and $$\sin(180)=0$$