Question

Find 3sqrt i

Answer 1

\[\sqrt[3]{i}\]

Answer 2

Draw it out in an Argand's diagram or however it's called because I can't spell

Answer 3

kenny can u help me after?

Answer 4

what is that diagram?

Answer 5

....I have no idea what that is suppose to be.... how do I graph the equation on that?

Answer 6

Wait, ignore what I've said, I've got another approach

Answer 7

Do you know the DeMorgan's theorem?

Answer 8

No I meant De Moivre's formula
https://en.wikipedia.org/wiki/De_Moivre's_formula

Answer 9

Express \(i\) in terms of \(\cos\theta+i\sin\theta\) first?

Answer 10

okay, but there's only a 3, I don't know how to start.

Answer 11

Express i in terms of cosθ+isinθ first, and I'll tell you what to do next

Answer 12

But thats what I dont understand. can you give me an example?

Answer 13

Okay, a table for you:
\[\begin{array}{rcl}
1&=&\mbox{cis}0^\circ\\
i&=&\mbox{cis}90^\circ\\
-1&=&\mbox{cis}180^\circ\\
-i&=&\mbox{cis}270^\circ
\end{array}\]

Answer 14

Where \(\mbox{cis}\theta=\cos\theta+i\sin\theta\)

Answer 15

It'd be best if you memorize this table

Answer 16

Okay so \[cis \theta=\cos \theta+ i \sin \theta\] what do I do after this with the original equation?

Answer 17

well...

Answer 18

If you read it carefully...

Answer 19

\(\mbox{cis}\theta=\cos\theta+i\sin\theta\) isn't an equation...

Answer 20

Okay I shouldn't have been that lazy, wait a minute

Answer 21

From what you said I got \[\sqrt{2}/3+1/2 i\] is that close?

Answer 22

\[\begin{array}{rcl}
1&=&\cos0^\circ+i\sin0^\circ\\
i&=&\cos90^\circ+i\sin90^\circ\\
-1&=&\cos180^\circ+i\sin180^\circ\\
-i&=&\cos270^\circ+i\sin270^\circ
\end{array}\]

Answer 23

This is the table

Answer 24

no wait \[\sqrt{3}/2+1/2 i\]

Answer 25

Wow that's a surprise I didn't expect

Answer 26

you to get the correct answer in the first try :)

Answer 27

Im' not bad at math when I understand it....I read through another definition that told me what to do with the original equation. Thanks for the help, I wouldn't have understood it without the table and stuff.

Answer 28

No problem :)