Question

Please help!!! Find Medal!!!
Find the cube roots of 8(cos 216° + i sin 216°)

Answer 1

@jdoe0001 @whpalmer4

Answer 2

@satellite73

Answer 3

what is the cubed root of 8?

Answer 4

2

Answer 5

good,
what is \(216\div3\)?

Answer 6

72

Answer 7

then one answer is \[2\left(\cos(72^\circ)+i\sin(72^\circ)\right)\]
easy right?

Answer 8

yes! how do I find the other ones?

Answer 9

ready to find the other ones?

Answer 10

what is
\(216+360\)? (we are going around the circle again)

Answer 11

576

Answer 12

ok i believe you
what is \(576\div3\)?

Answer 13

192

Answer 14

ok so answer 2 is \[2\left(\cos(192^\circ)+i\sin(192^\circ)\right)\]

Answer 15

lather, rinse, repeat
you only have to do it one more time

Answer 16

great! So would I add 720 to 216 and then divide by 3 to find the next one

Answer 17

yes

Answer 18

2(cos(312∘)+isin(312∘))

Answer 19

same as dividing the unit circle in to three parts, with 72 as one of them, but it is just as easy to keep adding 360

Answer 20

yes

Answer 21

see how easy that is?

Answer 22

Great! SO is that all?

Answer 23

Thank you so much!!

Answer 24

yes
that is pretty much the whole point of writing \(a+bi\) in trig form
otherwise this would be very very hard

Answer 25

yw