Elements in sets that are common

In summary, to find the set A∩B∩C, which is the intersection of A, B, and C, we need to find the roots of z^6=sqrt(3)+i and determine which ones have a positive real and imaginary part. This can be done by drawing a unit circle with a hexagon and identifying the regions that satisfy both conditions.
  • #1
ronho1234
34
0
let A={z|z^6=√3 + i} B=(z|Im(z)>0} and C={z|Re(z)>0} find A∩B∩C
the part previous to this qn asks me to find the roots of z^6 and I've already down that. but i have no idea how to proceed with this, so do i draw my unit ciorcle with the hexagon and then follow to see what regions satisfies with the other 2? please help
 
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  • #2
Can you show the roots of z^6=sqrt(3)+i? Because if you write them down you just need to decide which ones have Real part positive AND have imaginary part positive. That should not be too hard as w=a+bi has Re(w)>0 iff a>0 and Im(w)>0 iff b>0
 

What are elements in sets that are common?

Elements in sets that are common refer to the objects or values that are shared by two or more sets. These elements can be found in each of the sets and are considered to be part of their intersection.

How do you find the common elements between two sets?

To find the common elements between two sets, you can use the intersection operation. This involves comparing the elements in each set and identifying the ones that are present in both sets.

What is the symbol for intersection of sets?

The symbol for intersection of sets is ∩ (pronounced as "cap"). It is used to represent the common elements between two sets in set theory and mathematics.

Can there be more than one common element between two sets?

Yes, there can be more than one common element between two sets. If the sets have multiple elements in common, they will all be considered part of the intersection of the sets.

What is the difference between common elements and unique elements in sets?

Common elements refer to the objects or values that are shared by two or more sets, while unique elements are those that are present in only one set and not shared by any other set. In other words, common elements can be found in the intersection of sets, while unique elements can be found in the difference of sets.

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