HW 3, Problem 2.4.1

100 days ago by sbowen

z_1 = 8 z_2= 5+3*i z_3= 2 a=var("a"); solve(norm(z_1 - a)==norm(z_2 - a)==norm(z_3 - a),a) 
        
[a == 5]
[a == 5]
z_1 = -1 z_2= -2+i z_3= -3 a=var("a"); solve(norm(z_1 - a)==norm(z_2 - a)==norm(z_3 - a),a) 
        
[a == -2]
[a == -2]
z_1 = 0 z_2= 1+i z_3= 1-i a=var("a"); solve(norm(z_1 - a)==norm(z_2 - a)==norm(z_3 - a),a) 
        
[a == 1]
[a == 1]
z_1 = 1 z_2= -1 z_3= -i a=var("a"); solve(norm(z_1 - a)==norm(z_2 - a)==norm(z_3 - a),a) 
        
[a == 0]
[a == 0]
# This is obviously a line, so there will be no center. z_1 = 0 z_2= -i z_3= infinity a=var("a"); solve(norm(z_1 - a)==norm(z_2 - a)==norm(z_3 - a),a) 
        
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# This is obviously a line, so there will be no center. z_1 = -i z_2= 0 z_3= i a=var("a"); solve(norm(z_1 - a)==norm(z_2 - a)==norm(z_3 - a),a) 
        
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