Question

How do you find the cube root of -1+isqrt3?!?!?!

Answer 1

Is this the equation?\[\sqrt[3]{-1+i}\] or is it \[-1+i \sqrt{3}\]?

Answer 2

it is the bottom one

Answer 3

@Johnbc

Answer 4

So you need to find cube root of bottom one Johnbc gave you?

Answer 5

yes

Answer 6

You would need to convert −1+i√3 to cosθ + i sin θ form

Answer 7

rcosθ + i r sinθ*
You then would need to apply DeMoivre's Theorem
\(\Large [r(\cos\theta + i \sin\theta)]^n = r^n(\cos(n\theta) + i\sin(n\theta))\)

Do you know how to convert it to r (cosθ + i sinθ) form?

Answer 8

no i dont.... i tried but i think i messed it up a lot. @geerky42

Answer 9

hmm, we would need r and θ first. Do you know how to find r?

Answer 10

i think its \[r|z|=\sqrt(a^2+b^2)\]

Answer 11

@geerky42

Answer 12

i tried that but oh well ill show you:
\[-1+isqrt3\]
\[z=r(\cos \Theta+isin \Theta)\]
\[r|z|=\sqrt(a^2+b^2)\]
\[\sqrt(-1^2+(\sqrt3^2))\]
\[=\sqrt2\]

Answer 13

@geerky42