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
69
2
avatar

The complex numbers \(a\) and \(b \) satisfy \(a \overline{b} = -1 + 5i.\)Find \(\overline{a} b.\)

 Sep 8, 2019
 #1
avatar+103858 
+1

Let   a  =   m + ni

Let  b conjugate =     p  - qi  

 

So

 

a* (b conjugate)  =   (m + ni) (p - qi)  =  mp + (np - mq)i  + nq    =  (mp + nq) + (np - mq) i =   -1 + 5i 

 

mp + nq  =  -1

np - mq  = 5

 

And

 

a conjugate  =  m - ni

b =  p + qi

 

So

 

(a conjugate) * b  =    ( m - ni) ( p + qi)  = mp + (mq - np)i + nq  = ( mp + nq)  + (mq - np)i 

 

So

(mp + nq)  =  -1

(mq - np)  =  -5

 

So

 

(a conjugate)  * b   =    -1  - 5i

 

 

cool cool cool

 Sep 8, 2019
 #2
avatar+23133 
+1

The complex numbers a and b satisfy  \(a\overline{b} = -1 + 5i\).
Find \(\overline{a} b\).

 

\(\begin{array}{|rcll|} \hline a\overline{b} &=& -1 + 5i \\ \overline{a\overline{b}} &=& \overline{-1 + 5i} \quad | \quad \overline{a\overline{b}} = \overline{a}\overline{\overline{b}} \\ \overline{a}\overline{\overline{b}} &=& \overline{-1 + 5i} \quad | \quad \overline{a}\overline{\overline{b}} = \overline{a} b \\ \overline{a} b &=& \overline{-1 + 5i} \quad | \quad \overline{-1 + 5i} = -1 - 5i \\ \mathbf{\overline{a} b} &=& \mathbf{ -1 - 5i } \\ \hline \end{array}\)

 

laugh

 Sep 9, 2019

8 Online Users

avatar