plz help ....
Find all the eighth roots of (19 + 7 i)

Question

plz help ....
Find all the eighth roots of (19 + 7 i)

raden · Answer

eighth roots ?

anonymous · Answer

means all the roots starting from 0 to 7.... each and every root

terenzreignz · Answer

I don't that's what it means... I believe you're just tasked to find the eighth roots, and there are many of them...
Start by converting it into polar form, it's simple from there on...

raden · Answer

maybe u want to sum series of (19+7i) from 0 to 7 ??

terenzreignz · Answer

Well, then it all depends what you mean by
19 + 7i...
It sure looks like a complex number to me :D

anonymous · Answer

terenzreignz u mean (cos @ + i sin@) .....

anonymous · Answer

yes it is

terenzreignz · Answer

Yes, I do mean that, but you forgot the "r"
it's
r cis @

terenzreignz · Answer

Where
cis @ = cos@ + isin@

anonymous · Answer

like r^(19/7) (cos 19 + i sin 7)

terenzreignz · Answer

No, that's not how it works, I'm afraid :D
For your complex number
a + bi
can be written in polar form:
$$r(\cos \theta + i \sin \theta)$$
Where
$$r = \sqrt{a^{2}+b^{2}}$$
and
$$\theta = \tan^{-1}\frac{b}{a}$$(not as simple as it seems)

anonymous · Answer

ok then let me try this one ..... by the way tnx for the help..  :)

terenzreignz · Answer

Hold, on, before you go, keep this in mind, and think on it deeply...
$$\left[ r(\cos \theta + i \sin \theta) \right]^{p}=r^{p}(\cos p\theta + i \sin p\theta)$$

anonymous · Answer

My θ is 20.22 and r=sqrt410 ..... ?

anonymous · Answer

correct use radian for your theta=20.22 degrees