complex number

kring_c14

1. The problem statement, all variables and given/known data
find the four fourth roots of -2[tex]\sqrt{3}[/tex]+i2


i dont have any attempt for a solution because i dont know what to do..
im really lost.. i regret sleeping in class
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

HallsofIvy

I imagine you were intended to use DeMoivres' theorem:
If a complex number can be written in polar form [itex]z= r(cos(\theta)+ i sin(\theta))[/itex] then its nth power, zⁿ, can be written [itex]z^n= r^n(cos(n\theta)+ i sin(n\theta)[/itex]
In your case, n is the fraction 1/4. Convert [itex]-2\sqrt{3}+ 2i[/itex] to polar form (which happens to be pretty simple). Take the real fourth root of r. Remember that you can add any multiple of [itex]2\pi[/itex] to [itex]\theta[/itex]. Dividing by 1/4 will give you different results for different multiples of [itex]2\pi[/itex].

kring_c14

im having some problem in the angle..
what i dis is this

z=r cis (theta)
x=-2(sqrt3)
y=2
r=4
so
theta=-60

then, will i just substitute the numbers to the equation?

HallsofIvy

Yes, of course. r= 4 and theta= - 60 degrees (although I would prefer theta= -[itex]\pi/3[/itex]).

kring_c14

i think the angle is is -30...

soln:

x=-2(sqrt3)
y=2
r=4
tan (theta)= 2/[-2(sqrt3)]
=-1/sqrt3=-30degrees=-pi/6

shouldn't I make the angle positive????

if yes
should i subtract 30 from 180
or subtract 30 from 360?

i'm totally clueless...
desperately needing some help

kring_c14

pls pls pls...help me with this one..can anyone give me a complete solution for this???thanks

Dick

It looks to me like your angle is more like 150 degrees. You are in the second quadrant. So yes, subtract it from 180.