- #1

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## Homework Statement

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

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- Thread starter kring_c14
- Start date

- #1

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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

- #2

HallsofIvy

Science Advisor

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If a complex number can be written in polar form [itex]z= r(cos(\theta)+ i sin(\theta))[/itex] then its nth power, z

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].

- #3

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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?

- #4

HallsofIvy

Science Advisor

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

- #5

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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

- #6

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

- #7

Dick

Science Advisor

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