The denominator is 2+3i.  Its conjugate is 2-3i 

(change the sign of the term containing i)

Multiply by the unit fraction formed by putting the con=jugate
of the denominator over itself: 

·



Multiply (FOIL) out the top and bottom:



Combine the like terms. (the two middle terms in the bottom cancel)  



Substitute (-1) for i²



Simplify



Combine like terms:



Divide the -10 and the -11 each by 13





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Also, how would you find the equation of a circle with a diameter AB, given that the coordinates of a and B are (-6,1) and (4,-5). What is the answer in standard form:

We need the the radius r and the center (h,k) and then we can 
substitute thes is the equation for a circle:

(x - h)² + (y - k)² = r²

Let's graph the points and draw the diameter:



We will use the distance formula to find the diameter, which we will take
on half of for the radius. The distance formula is:

d = 

d =  =  =  =  = 

d =  =  = 

So the diameter is  and the radius is one-half of that 
diameter which is 
 
The midpoint of any diameter is the center.  So we use the midpoint formula:

Midpoint =  = 
 =  =  = 

So the center is (h,k) = C(-1,-2) and the radius is r = .

Substituting in

(x - h)² + (y - k)² = r²


(x - (-1))² + (y - (-2))² = ()²

(x + 1)² + (y + 2)² = 34




Edwin