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Determine the complex number z satisfying the equation \(2z-3i\bar{z}=-7+3i\). Note that \(\bar{z} \) denotes the conjugate of z.

 Apr 14, 2019
 #1
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2(a + bi)  - 3i ( a - bi)  = -7 + 3i

 

2a + 2bi - 3ai - 3b  = -7 +3i

 

Equate real and imaginary parts

 

(2a - 3b)  = 7    ⇒  6a - 9b  = 21

(-3a + 2b) = 3   ⇒  -6a + 4b = 6         

 

Add the last two equations   and we have

 

-5b = 27

b = -27/5

 

And  

 

2a - (3)(-27/5) =  7

 

2a + 81/5  = 35/5

2a = [ 35 -81] / 5

2a = -46 / 5

a = -46/10  = -23/5

 

So

 

z  =  -23/5  - (27/5) i

 

 

cool cool cool

 Apr 14, 2019

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