Question

Express the complex number in trigonometric form.

-4

Answer 1

will fan and medal

Answer 2

so first look on the unit circle where do you have there is a real part but no imaginary part

Answer 3

what point

Answer 4

you could actually two points from the unit circle but we only need one

Answer 5

ok

Answer 6

so what do i do?

Answer 7

what point on the unit circle has a real part but no imaginary part

Answer 8

i guess all of them are real with no imaginaries, right?

Answer 9

no

Answer 10

the x-axis is the real number axis
and the y-axis is the imaginary axis
in this scenario

Answer 11

(1,0) and (-1,0) both have a real but no imaginary part
also known as 1+0i or -1+0i

Answer 12

your number given is just a multiply of that

Answer 13

oh ok

Answer 14

what angle has cosine is 1 and sine is 0?

Answer 15

90 degrees

Answer 16

at 90 degrees we have cosine is 0 and sine is 1

Answer 17

oh wait, yeah youre right. its 0 degrees

Answer 18

cool stuff...
\[1+0i=\cos(0)+\sin(0)i\]
and multiply both sides by -4

or... you could have gone with
\[-1+0i=\cos(\pi)+\sin(\pi)i\]
and instead multiply both sides by 4

Answer 19

so would it be: 4(cos 0° + i sin 0°)
?

Answer 20

that is one possible answer out of many

Answer 21

but yes that works

Answer 22

i'm sorry

Answer 23

I missed you didn't put the -4 in

Answer 24

-4(cos(0)+i sin(0))

Answer 25

two answers out of many
-4(cos(0)+isin(0))
4(cos(pi)+isin(pi))

Answer 26

it also depends on what they want
do they want r>0
the magnitude number?

Answer 27

did they give any restrictions on r or the angle we choose

Answer 28

these were my possible answers:
4(cos 0° + i sin 0°)
4(cos 180° + i sin 180°)
4(cos 90° + i sin 90°)
4(cos 270° + i sin 270°)

Answer 29

oh well we definitely have your choice above
instead of using pi you could use...

Answer 30

180 deg...

Answer 31

pi rad=180 deg

Answer 32

\[-1+0i=\cos(180^ \circ)+\sin(180^\circ) i\]
multiply both sides by 4