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avatar+1110 

Determine the complex number satisfying the equation \(3z + 4i \overline{z} = 1 - 8\)i.

 Apr 14, 2019
 #1
avatar+100571 
+1

3z  +4i (z conjugate) = 1 - 81

 

3 ( a + bi)  - 4 i ( a - bi)  = 1 - 8i

 

3a + 3bi  - 4a i - 4b  = 1 - 8i

 

(3a - 4b) + (3b - 4a) i  = 1 - 8i

 

Equate coefficients  on real , imaginary parts

 

3a - 4b  = 1       ⇒  12a - 16b  = 4   

-4a + 3b  = - 8  ⇒  -12a + 9b  = -24          add the last two equations

 

-7 b = - 20      ⇒  b = 20/7

 

And 

3a - 4(20/7)  = 1

3a - 80/7 = 7/7

3a  = 87/7

a = 87/21  = 29/7

 

So

 

z   =    29/7  + (20/7) i

 

 

cool cool cool

 Apr 14, 2019
 #2
avatar+1110 
0

Sorry, but this is incorrect!

 Apr 14, 2019

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