Question

Express the complex number in trigonometric form.

-2i

Answer 1

-2i=-2(i)=-2(0+i)
=-2(0+i*1)
so when is cos 0 and sin 1 ?
or

look at this way
-2i=2(-i)=2(0-i)
=2(0-1*i)
so when is cos 0 and sin -1?

Answer 2

yes so for the bottom route you found theta to be 3pi/2

Answer 3

pi/2 or 3pi/2 ?

Answer 4

\[2(\cos(\frac{3 \pi}{2})+i \sin(\frac{3\pi}{2}))\]

Answer 5

Ok thank you

Answer 6

you could have went the top route too
\[-2(\cos(\frac{\pi}{2})+i \sin(\frac{\pi}{2}))\]

Answer 7

Can you help with one more?

Express the complex number in trigonometric form. (2 points)

3 - 3i

Answer 8

well first both terms have a three in common

Answer 9

3(1-i)

Answer 10

when are sin and cos opposites?

Answer 11

like you have cos is pos and sin is neg
so that means you are in the fourth quadrant
what angle in the fourth quadrant gives you sin and cos are not only difference in sign but are opposite values

Answer 12

2nd & 4th quadrants?

Answer 13

oh I think I got it

Answer 14

it would be 7pi/4 since we're in the 4th quadrant

Answer 15

great you see at 7pi/4
cos is -sqrt(2)/2 and sin is sqrt(2)/2
so but we have 3(1-i)
we can manipulate that
\[3 \frac{2}{ \sqrt{2}}( \frac{\sqrt{2}}{2}+i (-\frac{\sqrt{2}}{2})) \\ 3 \frac{2}{\sqrt{2}}(\cos(\frac{7 \pi}{4})+i \sin(\frac{7 \pi}{4}))\]

Answer 16

\[\frac{6}{\sqrt{2}}(\cos(\frac{7 \pi}{4})+i \sin(\frac{7 \pi}{4}))\]

Answer 17

Would the answer be
3*sqr rt(2) (cos7pi/4 + isin7pi/4)

Answer 18

if you choose to rationalize the outside factor's denominator yep

Answer 19

Ok also in the beginning how did you know that the cosine and sine would be opposites? Like in order to find out what quadrant it would be in.

Answer 20

we have 1-1i

Answer 21

1 and -1 are opposites

Answer 22

correcting type-o above:
great you see at 7pi/4
cos is sqrt(2)/2 and sin is -sqrt(2)/2

Answer 23

Oh okay

Answer 24

if you don't like that I could show you another way

Answer 25

No I understand.

Thank you

Answer 26

3-3i
draw visual


\[3 \sqrt{2}(\cos(\frac{-\pi}{4})+i \sin(\frac{-\pi}{4}))\]
this answer looks a little difference because I describe theta a little differently but the trig forms or still equal