Question

Express the complex number in trigonometric form.

-6i

Answer 1

\(-i\) means \(\theta =3\pi/2\) and \(6\) means \(r=6\).

Answer 2

@wio so how would i put that into one statement

Answer 3

6(cos 0° + i sin 0°)

6(cos 270° + i sin 270°)

6(cos 180° + i sin 180°)

6(cos 90° + i sin 90°)

those are the answer choices and their formats

Answer 4

Are you phoning this one in? What class is this?

Answer 5

it's pre-calc I read through the lesson, but i'm still confused as to how to get from point a (the number) to point b (the final form)

Answer 6

Basically, \((a,b)\) are the Cartesian coordinates, and \((r,\theta)\) are the polar coordinates.
\[
a+bi = re^{i\theta} = r[\cos\theta+i\sin\theta]
\]

Answer 7

In our case, we have \((a,b) = (0,-6)\). We want \((r,\theta)\).

Answer 8

\[
r= \sqrt{a^2+b^2} \\
\theta = \arctan\left(\frac ba\right)
\]

Answer 9

In this case, since \(a=0\), we have to remember that \((0,-6)\) it directly under the origin, that's a trivial angle to find.

Answer 10

alternatively, use the fact that \(\cos(\theta) = 0\) and \(i\sin(\theta) = -1\).

Answer 11

How would you find theta if a=0 then, is there a special case for it?

Answer 12

When \(a=0\), that means \(\cos\theta = 0\).
So \(\theta\) must be \(\pi/2\) or \(3\pi/2\).

Answer 13

and how can you tell which one it is?

Answer 14

\(b>0\implies \theta = \pi/2\). \(b<0 \implies \theta =3\pi/2\). Did you read what I wrote and drew before?

Answer 15

yes, so it would be 3pi/2

Answer 16

which i guess makes the answer B? 6[cos270+isin270]

Answer 17

Yes

Answer 18

thank you for your help!