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

 Apr 25, 2019
 #2
avatar+2557 
+1

Um... I'm only in 7th grade so I just going to solve WITHOUT the complex conjugate and Zbar thingy just for the fun of it.

 

1. Sqaure both sides.

 

9z^2-4z^2=1+8

 

9z^2-4z^2=9

 

5z^2=9

 

z^2=9/5

 

\(\boxed{z=\frac{\sqrt{9}}{5}}\)

.
 Apr 25, 2019
 #3
avatar+106535 
+1

3z + 4iz'  = 1 - 8i

 

3 (a + bi) + 4i(a - bi)   = 1 - 8i

 

3a + 3bi + 4ai + 4b  = 1 - 8i

 

3a+ 4b =  1      ⇒   12a + 16b  = 4

4a + 3b  = - 8 ⇒     -12a - 9b = 24

 

7b  = 28

b = 4        and   3a + 4(4) = 1   ⇒  3a = - 15  ⇒  a = -5

 

So

 

z = -5 + 4i

 

cool cool cool

 Apr 25, 2019
 #4
avatar+166 
+2

Thank you

FlyEaglesFly  Apr 26, 2019

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