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\((a+bi)^2=2(a-bi)\)

 Dec 1, 2018
 #1
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(a + bi)^2  = 2( a - bi)

 

 

 

a^2 + 2abi - b^2 =  2a - 2bi

 

Equating the real and imaginary parts, we have that

 

(a^2 - b^2) = 2a              2abi = - 2bi

 

Using the second equation

2a = -2

a = -1

 

 

And using the first equation

 

(-1)^2 - b^2 = -2

-b^2 = -3

b^2 = 3

b = ±3

 

 

cool cool cool

 Dec 1, 2018

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