1. ## complex numbers

During my university course my instructor has taught us how to do the following type of question and I understand how to do it..
Evaluate square root of z z=-5+j12 then using Pythagoras and trig the angle comes out at 13<1.966 rads.
< = angle.
Using the following formula z^1/2 = 13^1/2 <(tan^-1 12/5 +k2pie)/2 and letting k = 0 and 1 respectively I eventually come up with 1.999 + j3.001 and -1.999 – j3.001 as my roots of the above question..
I understand this..
However I now have the question find the roots of complex number z^4= 1-sqrt 3
In this instance do I do the same as above..
i.e r = sqrt (1^2+(sqrt3)^2) =2 Theta =2pie – tan^-1 sqrt3/1 = 5.236 rads.
Let k=0 z^4= 2^4<(5.236 + (0 * 2pie)*4 = 20.944
= 16<20.944 I need to divide this by 2pie to fit into a circle
= 16 < 3.333
Using the formula r(cos theta + j sin theta) this = -15.717 – j 2.997
Following rest through using the above method, k=1,2,3 respectively I get
16<1.050 giving 7.961 +j 13.879
16<5.05 giving 5.299-j 15.098
16<0.267 giving 15.346 + j4.53
Is this the correct method to use to tackle this problem.. Any advice will be greatly appreciated.

2. Originally Posted by jawa7539
During my university course my instructor has taught us how to do the following type of question and I understand how to do it..
Evaluate square root of z z=-5+j12 then using Pythagoras and trig the angle comes out at 13<1.966 rads.
< = angle.
Using the following formula z^1/2 = 13^1/2 <(tan^-1 12/5 +k2pie)/2 and letting k = 0 and 1 respectively I eventually come up with 1.999 + j3.001 and -1.999 – j3.001 as my roots of the above question..
I understand this..
However I now have the question find the roots of complex number z^4= 1-sqrt 3
In this instance do I do the same as above..
i.e r = sqrt (1^2+(sqrt3)^2) =2 Theta =2pie – tan^-1 sqrt3/1 = 5.236 rads.
Let k=0 z^4= 2^4<(5.236 + (0 * 2pie)*4 = 20.944
= 16<20.944 I need to divide this by 2pie to fit into a circle
= 16 < 3.333
Using the formula r(cos theta + j sin theta) this = -15.717 – j 2.997
Following rest through using the above method, k=1,2,3 respectively I get
16<1.050 giving 7.961 +j 13.879
16<5.05 giving 5.299-j 15.098
16<0.267 giving 15.346 + j4.53
Is this the correct method to use to tackle this problem.. Any advice will be greatly appreciated.
It is hard to read this. Is the question find $\sqrt{12i-5}$?