It is hard to read this. Is the question find ?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.
Many thanks in advance