find i ^ (1/3)

Question

find i ^ (1/3)

fibonaccichick666 · Answer

so write it in exponential form

fibonaccichick666 · Answer

to start

anonymous · Answer

ok, can you please show me how?

fibonaccichick666 · Answer

how do you express i in exponential form?

anonymous · Answer

i am not sure, is it '1'

anonymous · Answer

please help!

anonymous · Answer

???

kainui · Answer

$$e^{i \theta} = \cos \theta + i \sin \theta$$ So what value of theta will set the cosine term to 0 and the sine term to 1? That'll be the same thing as i, right?

anonymous · Answer

thank you so much for responding! i got -i

anonymous · Answer

normally if its a whole number you can divide by 4 and then see what your remainder is and go from there, but since this is a fraction it threw me off... is my answer correct?

kainui · Answer

Well, technically there are 3 roots to a cube root, so this is indeed one of them since (-i)^3=i

anonymous · Answer

https://lss.brainhoney.com/Resource/12022823,CA,2F,0/Assets/quiz/Po-Unit3Exam/img22.gif

anonymous · Answer

can you view this?

anonymous · Answer

because I'm thinking maybe you are misinterpreting my question... I'm sorry I might not have written it out correctly, but what you see in the link is correct

kainui · Answer

Nope, I think I'm interpreting it correctly. =)

kainui · Answer

For example, for a square root, there are two answers right? like (-2)^2 =4 and (2)^2=4 right? Similarly for a cube root you will have 3 roots.