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If (a + bi)^2 = b + ai, where i^2 = -1, and a and b are positive, then find (a,b).

 Dec 31, 2019
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(a + bi)^2   =  b +  ai

 

a^2  + 2abi  +  (bi)^2  = b + ai

 

a^2 + 2abi  - b^2   =   b + ai

 

Equating terms  we have that

 

2abi  =  ai

2b  =  1

b = 1/2

 

And

 

a^2 - b^2  =  b

a^2  -  (1/4)  = (1/2)

a^2 =  3/4

a = √3 / 2

 

So

 

(a,b)    =  ( √3 / 2 ,  1 / 2  )

 

 

cool cool cool

 Dec 31, 2019

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