We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
171
4
avatar+166 

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

 Apr 25, 2019
 #2
avatar+2363 
+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+104836 
+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

10 Online Users

avatar