1. ## intersecting sets

Let A = {z|z6 = '3 + i} and B = {z|Im(z) > 0} and C = {z|Re(z) > 0
(where '3 means the square root of 3)

.. I found the z6 to be: (using k = 0,1,2,3,4,5 in that order)

z1= z1/6(cos pi/6 + isin pi/6)
z2= z1/6(cos 2/pi + isin 2/pi)
z3= z1/6(cos 5pi/6 + isin 5pi/6)
z4= z1/6(cos 7pi/6 + ison 7pi/6)
z5= z1/6(cos 9pi/6 + isin 9pi/6)
z6=z1/6(cos 11pi/6 + isin 11pi/6)

I've been asked to find the 'intersecting' of sets A, B, and C.. But not really sure how I'm meant to compapre real, imaginary and complex numbers together..

2. ## Re: intersecting sets

Now that you have figured out the set A(which is not entirely correct,please look at it again),choose only those elements which have their real and imaginary parts greater than 0.In short both cos and sin terms should be positive.

3. ## Re: intersecting sets

but does that mean I pretty much write my answer out to set A again..

Literally :

z1= z1/6(cos pi/6 + isin pi/6)
z2= z1/6(cos 2/pi + isin 2/pi)
z3= z1/6(cos 5pi/6 + isin 5pi/6)
z4= z1/6(cos 7pi/6 + ison 7pi/6)
z5= z1/6(cos 9pi/6 + isin 9pi/6)
z6=z1/6(cos 11pi/6 + isin 11pi/6)

4. ## Re: intersecting sets

Go through this once:Complex number - Wikipedia, the free encyclopedia

Intersection of Sets B and C gives you the first quardant.Consider only those z which lie in first quadrant and satisfy condition of set A.

5. ## Re: intersecting sets

thanks a billion, that makes alot of sense !