SOLUTION: (a+bi)^2=i determine a and b must be real numbers

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Question 1074213: (a+bi)^2=i
determine a and b
must be real numbers

Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!






Since i2 = -1





Set the real part of the left side equal to the real
part of the right side:

and

Set the imaginary part of the left side equal to the 
imaginary part of the right side:
 
  and  
                      
                      

Substitute for b in







; 
;   
;  

; 
; ignore the imaginary value for a
Substitute in:


 
 


So there are two solutions:

; 

One solution is where a and b are both positive,
and the other solution is when they are both
negative.

Edwin

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