Question

Find all of the complex cube roots
1 + i

Answer 1

would you sue the nth roots theorem for this problem? or De Moivre's Theorem?

Answer 2

*would you start

Answer 3

first write this in polar form, that will help
do you know how to find the absolute value and the angle?

Answer 4

\[|a+bi|=\sqrt{a^2+b^2}\] and in your case it is \(|1+i|=\sqrt{1^2+1^2}=\sqrt2\)

Answer 5

then you need the angle

Answer 6

yes for polar i had: z= √2 (cosπ/4 + i sinπ/4)

Answer 7

oooh then you are completely done almost
that is the hard part

Answer 8

would i use the nth roots theorem for this one? or the de moivre's theorem? i think its nth roots??

Answer 9

divide the angle by 3, and take the real cubed root of the absolute value

Answer 10

same thing

Answer 11

nth roots?

Answer 12

\[\sqrt[6]{2}\left(\cos(\frac{\pi}{12})+i\sin(\frac{\pi}{12})\right)\] for the first one

Answer 13

there will be 3 answers right?

Answer 14

i dunno
i only ever heard of demoive, not the "nth root theorem"
yeas, there are three

Answer 15

once you have one you have them all, divide the circle up in to three equal parts
either that, or rewrite
\[\sqrt2\left(\cos(\frac{\pi}{4})+i\sin(\frac{\pi}{4})\right)\] and
\[\sqrt2\left(\cos(\frac{9\pi}{4})+i\sin(\frac{9\pi}{4})\right)\] and start again

Answer 16

i.e add \(2\pi\) to the angle, then divide by 3
then repeat one more time to find the third one

Answer 17

can i tell you wht i got for my 3 answers? and then can you tell me if theyre right?

Answer 18

z1= 3.066+ i 0.822
z2= 1.587 + i 2.750

Answer 19

z3= -0.822 - i 3.067

Answer 20

ARE my answers right? anyone??