Question

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°)

Answer 1

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°

Answer 2

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

Answer 3

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

Answer 4

What is that formula called? @peachpi

Answer 5

oh yeah. forgot about the negative

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

@satellite73

Answer 11

it is an equality between two numbers
you have \(-2\) right?

Answer 12

the absolute value of \(-2\) is \(2\)

Answer 13

Right @satellite73

Answer 14

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 \(2\times -1=-2\)

Answer 15

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