# Thread: Cubed roots of complex numbers in polar form

1. ## Cubed roots of complex numbers in polar form

I am taking a power series and matrices class and as part of the review we are being asked to determine the possible polar angles if we have the cube roots of 1 + i

I am at a complete loss as to how to tackle this. Would I just use r = the square root of (1^1/3 + 1^1/3) since the coefficient for i is one

and then use polar form: z = r cos angle + i r sin angle?????

Thanks to all of you who take time to help out struggling math students!!! Frostking

2. Originally Posted by Frostking
I am taking a power series and matrices class and as part of the review we are being asked to determine the possible polar angles if we have the cube roots of 1 + i

I am at a complete loss as to how to tackle this. Would I just use r = the square root of (1^1/3 + 1^1/3) since the coefficient for i is one

and then use polar form: z = r cos angle + i r sin angle?????

Thanks to all of you who take time to help out struggling math students!!! Frostking
$\displaystyle 1 + i = \sqrt{2} \text{cis} \left( \frac{\pi}{4} + 2n\pi\right)$. Take the cube root and then substitute n = 0, 1 and 2 to get the arguments.

3. Just to clarify, "cis(x)" is "engineering speak" for cos(x)+ i sin(x).

4. Originally Posted by HallsofIvy
Just to clarify, "cis(x)" is "engineering speak" for cos(x)+ i sin(x).
Which is fascinating since engineers use j to represent $\displaystyle \sqrt{-1}$ (i could get confused with the symbol for current. And it may surprise some viewers that there is a very strong link between electrical circuit theory and complex numbers).