Complex number help?

[Yoda]

Need help with the following question

 Find the solutions to the equation z^4 -2z^2+4=0 in polar form.

[hobbitle]

Hey mate,

I might not be doing this the most efficient way but this is how I'd do it (I won't type out all the steps because cfg using TeX, sorry)...

Let
-->
Solve using quadratic formula, you get:

Convert this to polar form using standard triangles to find the modulus and argument (modulus=2, argument=pi/3)

The result is the solution for z^2 so I guess you just take the sqrt of that to get your final answer.  I dunno i've been on holiday for like 3 months my brain is pretty dead.

[scribble]

(Sorry for the bad lighting)

[hobbitle]

^ what she did

[Yoda]

Thanks very much, but can you please explain how you did the last line?

[Stevensmay]

Last step is just an application of De Moivre's theorem which states that if

then


So in this question we have


And applying De Moivre's


Therefore



The other two solutions produced by square rooting are just those with complementary? angles.